Hello Noah,
I’ve been following this thread for about two weeks now (though there are way too many replies for me to read them all!). Since you asked this question weeks ago – I’m late to the party – it may have been answered to your satisfaction already. But I’d still like to offer some thoughts. I know this is a bit lengthy; hopefully you find it thorough rather than just verbose. 
(Side comment: my discussion below assumes, along with the BioLogos Forum expectations, orthodox Christian faith. In particular, I assume the truth of the Bible and its authority in our lives. In fact, I think the Bible ought to be foundational, rather than our beliefs sitting in the judge’s seat over Biblical teaching. For clarity of the discussion’s progression, I sometimes structure my comments in a way that may seem like we arrive at our beliefs first and Scripture is just supplemental, though that isn’t the “direction” I think it should go. I realize these are debated issues and require greater elaboration, but they are probably best handled elsewhere if they are “hang-ups.”)
I think there are actually multiple questions in your original post which, though related, are best treated separately. The ones I see are:
- whether or not (human) morality is objective;
- the ultimate source of morality;
- the immediate source of morality, including the mechanism(s) by which humans come to know morality (evolution, a direct divine impartation, etc.). This could also include the question about morality being unique to humans or not;
- a broader theme of reconciling evolution and Christian faith.
Each of these questions demand lengthier answers than is practical here. Many replies have already given various viewpoints, so my words here, at times echoing some of the previous replies, may seem like oversimplifications. If so, we could follow up on the “holes.” Anyway, here we go…
On #1: It would be useful to start by ensuring that we mean the same thing when we use the keyword “objective.” I think a good working definition is this: morality would be objective if it is defined by something (or someone!) entirely independent of and external to human existence and human purview. This seems to me to be what is most often meant when someone calls morality “objective” (I don’t think I’m playing artificial semantic games here), but I’m open to improvements to my definition. One implication of an objective morality, in this sense, would be that humanity could not take credit for “inventing” morality.
Anyhow, assuming for now that you accept my definition, the real question is whether or not morality is indeed objective. I think there are many Biblical principles which teach us that, at its core, the answer is yes; specifically, it is defined by God, who is in no way dependent on anything in the universe (His “divine aseity”). I think it would be difficult to take the Bible as a whole and conclude otherwise. But I am not so naïve as to think that no one has tried!
So, consider the book of Leviticus, which gives the Law, most certainly told to us to be from God, and equates keeping that Law with holiness – essentially a state of moral perfection (of course, we can’t achieve holiness on our own, which is why we need Jesus’ righteousness imputed to us in order to be reconciled to God). Variations of the command for people to “be holy for I am [God is] holy” appear several times in that book. Thus, human holiness is defined in terms of the holiness of God, and therefore all human morality would be defined by Him. (Side comment: the question of whether that holiness is defined directly by God’s nature or whether it is defined by His commands to us need not be answered to accept this latter conclusion; in both cases, it would still be correct to say that holiness, and thus morality, is defined by Him).
On #2: My comments on #1 have now partially answered this already. I’ll echo again that human understanding of morality can ultimately be traced back to God, though perhaps after some number of intermediate steps (which gets at #3). While on the topic, let me add some more Scripture. For example, in Jeremiah 31:33, God says He will put His law in the minds of the people of Israel and write it on their hearts, so He is given credit for His people knowing (understanding) His Law, and, in light of #1, morality. And in Micah 6:8, God is the one who shows us mortals what is good. Psalm 119 speaks clearly about the Law (again a proxy for morality) belonging to God, calling it righteous and eternal – see verse 160 for example – among other laudable superlatives. God is the source of morality, and again because of His divine aseity, He must be the ultimate source. (One implication: we dare not make light of the importance of morality in our own lives, as some are wont to do, since it is ultimately from God and isn’t merely a human construct.)
On #3: Well, in short, I don’t know. But I think it can have multiple answers at different levels of a “local/global” distinction. Following my comments on #2, God must be sovereign over the whole enterprise – “globally” – or else we would run into the problem of either contradicting Biblical teaching or even having no basis for objective morals at all (I haven’t argued that latter point here, though I do believe it). But the immediate – “local” – explanation for how a particular person has come to know morality might possibly be some mechanism (like a physical process) that, on its surface, seems to be independent of God. How could both be true? I’ve heard John Lennox give a good analogy which I will paraphrase and hijack for my purposes here (he was talking about different meanings of the word “why,” I think, so it wasn’t quite our context, but the point still applies). Imagine you walk into my kitchen to see a tea kettle on the stove with water boiling in it. You could ask why the water is boiling. The “local” reason has to do with the heat transferred into the water from the kettle, which itself comes from the stove, which itself comes from…and so on. But the “global” reason (overseeing the other steps in the process) is simply that I would like some tea! Both explanations are correct as far as they go. My point here, as some have said above, is that our morals ultimately coming from God doesn’t preclude them from coming from a seemingly different source simultaneously. This doesn’t exactly answer #3, but it seems to at least get it inside a more manageably sized fence. 
On #4: As I am less knowledgeable about evolution than many/most on this forum, I will only say that I believe such a reconciliation is possible, and I hope you don’t give up on finding one if that topic irks you.
Now, with all of that said, I have a few more general thoughts that I’ve been returning to as I reflected on this thread; they’re based more on the second half of your post. I preface this by asking you to read it as intended; it could appear like a “dodge,” especially over this somewhat impersonal medium, but I definitely do not mean it that way. I intend it sincerely, at face value.
Anyway, the main thought is basically the “practical response” that one could give to any question: if you could find a definitive answer to your original question, a surefire and incontrovertible resolution, what would it change in your day-to-day life or in your faith journey? If, in particular, evolution is simply a tool in God’s hands, then, speaking for myself, I think an answer would change virtually nothing in my life. It certainly wouldn’t affect my moral choices (since the question isn’t about what constitutes correct morality; rather, it’s about where morality comes from and how we come to know it), and would have only minimal impact on my internal view of morality (since, given the discussion above, I am already convinced of the ultimate source and standard of morality coming from God, then understanding how it “trickles down” to me has much less practical impact). And, again speaking for myself, if it would change so little, then it wouldn’t be of primary importance to me.
I wanted to bring this point up only because you said your question bothers you to an extreme. Of course I don’t say this to dismiss your question; it’s worthwhile to discuss, particularly if you sincerely find that it bothers you. If all truth belongs to God, as I believe it does, then we ought not shy away from asking honest questions, and I don’t believe God discourages such honest questions (asking questions as veiled challenges is another matter, but I see no reason to think that that is what you are doing!). Indeed, many on this forum have expressed their frustration, even to the point of damaging their faith, with past experiences of their questions which were dismissed with perfunctory “answers” or without any discussion at all – I’m in no way advocating for such a dismissal of the questions in your post. I just think it’s important to distinguish between things that are primary and secondary (and tertiary and beyond). Since I find this particular topic secondary or lower, I encourage you to reflect honestly on the question of what difference an answer would make, especially considering the possibility that an irrefutable answer might be out of humanity’s reach. Perhaps doing so would lessen the question’s urgency in your mind. And actually, if you’re still reading at this point, I’d be curious to hear from you, if you’re willing to share, what specifically about this question is bothering you. I’m wondering if you can identify why it bothers you to the extreme.
By the way, more generally I think that asking yourself metacognitive questions like this one (the “why do I care?” or “what difference would it make?” kind of questions) is tremendously useful in exposing presuppositions, assumptions, or motives that you might not even have known were there. What about “Issue X” stirs you more than other questions of faith and science? Do you find that you want a particular answer to be true? That can reveal something about your presuppositions (we all have them; I think that “unbiased neutrality” isn’t possible in these matters for an actual human, but that is another topic) and might impact which questions you ascribe more or less importance to. In fact, I see you’re already self-aware enough to do this, as you recognized that, in this case, your question came from an “impulsive skeptic” side of you. I’d be interested to hear more about what precisely you mean by that. Either way, considering more deeply the source of this (or any) question will be worth your time, in my opinion.
Regardless, I hope you’re able to find an answer that satisfies you and, most importantly, draws you closer to Christ, thinking more of His thoughts after Him. In the meantime, keep asking questions, and keep “seeking first His Kingdom and His righteousness” (Matthew 6:33).