The transaction to your address took place about half a year before I learned about Bitcoin and I don't know which wallets besides Bitcoin-GUI were common or popular around July 2010. So, lets assume you used Bitcoin-GUI, because I'm not aware of any deterministic wallet around that time. Armory came later and its recovery and chain key did look very different from what you describe.
As far as I remember if you did export a private key of your receiving address then Bitcoin-GUI would've given you a private key in WIF format (not 100% sure about this as I didn't do such things with Bitcoin-GUI in 2011 when I first used it). What you say about your characters doesn't appear as a WIF key, so it might be that you converted it to hex for some reason (maybe as a decoy).
Are you absolutely sure, you don't have any sort of documentation about your "backup"? If not, as a reminder to other readers, stay away from selfmade obfuscation or backup methods without documenting it properly. There's very likely lots of footguns with such approaches.
I don't quite get or can visualize what you mean by "The question marks are sort of spread around the first half of the characters and aren't in the beginning or end." and together with "I stacked they string of characters in a way I couldn't tell if it was two 40 character keys or an 80 character key. If I only use the top line I have a 40 character string with no question marks, but that is an odd length.".
A private key in hex is 64 characters. You have 66 if we ignore the purpose of the questions marks (could be a decoy). You say your hex string starts with "001", so what about if you drop the leading "00" which would give you remaining 64 hex chars and try to use that as a hex private key. Also try your 64 char hex string in reverse! Who knows what "crazy" scheme you invented? No pun intended, just being mildly creative...
I have some other idea if you would explain me in more details what you mean by "The question marks are sort of spread around the first half of the characters and aren't in the beginning or end.".
From what I understood so far, the question marks don't replace any missing hex characters as you say you have all of them, 0...F, in the written characters already. 14 missing characters hidden by the question marks would be a bit too long to remember, except if they hide something like a regular series like ascending or descending hex digits.
When you say you wrote blocks of four hex characters: where do the question marks appear in the blocks where they are?
BTW, what do you get in terms of number of hex characters when you completely discard the blocks which have a question mark in them? Could this give you a mini private key? Hm, I'm just brainstorming, but I find this a bit odd to assume you used a mini private key as that would've required external tools to create one. Not sure how good your memory is roughly 13 years ago.