Hey everyone -
Quick update:
I found a pair of Hutchinson 26x2.00 Python Air Light tires which the seller on eBay marketed as "tubeless." Turns out, they are not the tubeless version and of course the guy on eBay is being an ass about it, but they do seem to work (for now).
I was able to do the conversion yesterday. I still haven't ridden the bike as I'm still working on the drivetrain, but they do seem to hold air. It was a bit of a PITA to get the tires to seal. The rear wheel sealed up on first attempted without any soapy water and without removing the valve core, but the valve stem kept leaking (I was doing the ghetto cut an old tube and use that valve stem approach). I bought a set of Stan's valve stems today and solved that issue.
The front wheel was an enormous pain as it just did NOT want to seat itself. I was using my Blackburn Chamber pump and even with the blast of air I couldn't get the bead in there. Eventually, after lots of pumping up that chamber, I was finally able to get it to seal. I left both wheel horizontal overnight and found the pressure to be the same this morning.
I'm a little nervous to see if they will hold when I actually ride them as neither the tires nor the rims are tubeless ready, but they do seem to be holding for now.
Thanks for all the help!