This will be a fun conversation.
I have some important qualifications to make here before we dive in.
First, I am broadly speaking in the BioLogos "tent", but this is question to me so I will tell you what I personally believe on these things. In the same way that you disagree with other YECs about important points, I also disagree with other theistic evolutionists (TE) and evolutionary creationists (EC) about important things too. In this conversation I will speak for myself. BioLogos has its own, limited belief statement if you are curious of their position: http://biologos.org/about-us/.
With that, it is quite easy to find TEs that disagree with me (like Kenneth Miller) and visa versa. Even here on the forums, I can identify important disagreements between my friend @DennisVenema and myself. So let's try and avoid the assumption that either of us automatically agree with everyone in our respective "camps." I know I do not, and (given the diversity of the YEC camp) I am sure you do not agree on everything of importance with everyone in your camp either.
I'll start with a statement of my belief.
I am an Evangelical Christian. I affirm the historic creeds (Apostles and Nicene) and the more recently written Lausanne Covenant (https://www.lausanne.org/content/covenant/lausanne-covenant). I also affirm the intended meaning of BioLogos' belief statement http://biologos.org/about-us/, though I do dispute some of the vocabulary.
I believe that Jesus bodily rose from the dead by an act of God in this world to reveal Himself to all mankind. I respond with belief to this self-declaration that God exists, is good, and wants to be known. Because of this historical fact, I trust the Bible as God's authoritative written word to all of us. The One who rose from the dead is entirely able to preserve His written message to us through history.
From Scripture, then, I believe that God created us; He designed us all. With providential purpose, forethought and care He brought us all into existence. According to Scripture, his way of doing this was not instantaneous and was part of a process; He asked the the land to "give forth" many kinds of life (Genesis 1:24), which tells us something about what the land is capable of doing, and that this is still dependent on His calling.
Next, he created Adam and Eve; historical people that existed in space and time in our past, and all of us trace our lineage to them. According to Scripture, He did not make them out of nothing, popping them into existence. Rather, He made Adam from the "dust of the earth" and Eve from Adam's "rib." We are in "God's image", but we are also of the "dust".
He created them as the first beings capable of communion with Him. It was good for a time, but not perfect. Then, moving from naivety they chose to understand Good and Evil for themselves, and this brought them into accountability and judgement for their sin. The same judgement that we all live under now, if not for the grace demonstrated to us through Jesus. The ultimate end of mankind remains the same at is was in the beginning, to enter into communion with God.
The God in Scripture providentially governs all things. Nothing is beyond His sight or His reach. This includes the process by which the "land gave forth" life of many kinds. We discuss and mathematically model randomness in lots, poker and dice, knowing that we speak from a human perspective. God knows the outcome of all these random events, and governs them according to his providential concerns that we do not understand. In the same way, we discuss "randomness" in the land's giving forth (i.e. evolution), but this is a limited statement from a purely human point of view. What is random to us, is known to God. He providentially governs all things.
We can suppose about different worlds (https://discourse.biologos.org/t/a-world-where-neanderthals-survived-till-now/35130), but ultimately, we are only given this world and can only understand God clearly through what He chooses to reveal to us. No human effort can bring us to HIm, not even science. We are totally dependent on His self-revelation.
And in this world, we find that revelation in the living Word: the life, death, and resurrection of Jesus. Let us all follow him.
Of course there is much to discuss from here. But this is my statement of belief.