I'm with you on all but the last part; I don't think we can say that the Bible says Adam was created 6036 years ago.
I have to assume you're using "the begats" and estimating the time span for a generation there?
I understand the original Hebrew verb "to beget" did not always have to mean the direct parent, but rather lineage.
That is, a grandfather can be said to have begotten a grandchild. Or great grandchild.
I also think God purposefully hid the exact ages of these things, just as He does wish us at this time to find the actual cross or other such artifacts.
For one, unbelievers would still not believe it, even if their names were written in the stars.
For another, I think God still wants us to take these things on faith for now.