Zack,
Sounds like you want a challenge and that you're on a somewhat restrictive budget. I'd guess that for around 10-12k you can put together a T206 set minus the big 4. But you've gotta be willing to deal with some pretty ugly cards -- especially for Demmitt, O'hara and Cobb Green.
If it was me, I'd budget a little more ... say $15-20k and do it over a many year period. that amount should enable you to get cards that are around the "Fair/Good" level. Don't worry about the different backs at all, and be willing to accept creasing, trimming or some back damage (but at that price you shouldn't need to buy cards with pieces missing). Since Demmitt and O'hara alone can run close to 2k for the pair, I'd push that off till the end -- unless a deal that you can't pass up comes along.
As for my dad and I, we're putting together a raw set that a minimum vg/ex. We get so much more pleasure looking at the cards in a binder instead of plastic slabs. We're probably about 50 cards away from completing it in any shape (and about 120 cards from completing it in vg/ex or better).
Best regards and enjoy the journey - it's a very, very fun challenge!
-S
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