I'm not intentionally trying to put words in your mouth. The exercise is an attempt to see if the intersection of your two premises is a conclusion you actually didn't want to make.
My reference to the Roman Catholics is purely to counter-poise the RC traditions with the Eastern Orthodox. It is relatively universally accepted that the Roman position is based on Augustine's analysis. But I will be more careful about making it sound like Augustine had a made an official choice that he never actually needed to make.
So, you re-phrased your position to include:
"I am not saying that the doctrine of Original sin means "only" that they have a sin nature, but that they have already sinned, in the womb."
well, this is what I thought your position already was. It was your writing: "It is much worse than that. It is the idea that Adam's sin so corrupted the race that all his descendants are born (apologies for the double negative) with the inability not to sin."
I'm not sure you even bother with this position, if you have already acepted the next sentence you wrote: "But the sins we are charged with, presumably even dead infants, are their own, not Adam's."
So, let me attempt a paraphrase again, especially in view of your interpretation of Psalms 51:5:
Psalms 51:5, NIV:
"Surely I was sinful at birth, sinful from the time my mother conceived me. "
"Infants require baptism because infants have non-consciously sinned in the womb."
That's a pretty empatic assertion (I'm a pretty emphatic guy; I like empatic. So for the purposes of this thread, there is no sin in being emphatic!
But let's look Psalms 51:5! You understand that the NIV interpretation is not the "usual one", right?
King James has it thus:
Psa 51:5: "Behold, I was shapen in iniquity; and in sin did my mother conceive me."
And that's a completely different kettle of fish, yes @heddie ?