So it's currently at 135mm (my guess is that it's not, but had a 135mm hub shoved between the dropouts) and you're suggesting to cold set it again to 126mm? What sense does that make?

OP, your Trek 720 has long chain stays and if the spacing at rest is right around 130 you're golden. A 130mm road hub will let you run Shimano/SRAM compatible 7-10 speed cassettes. The Deore mechs will work famously in friction mode with some bar end shifters. You're on your way to having a nice setup.