Ive ridden the first two sections (from Denver) on a rigid bike, fully loaded. (4 pans, lowriders in front, etc.) using schwalbe marathon supreme 1.6 inch tires....
The front lowriders were a problem for clearance issues. the rear panniers were no problem. Highrider front bags would have helped.
I used drop bars which were not ideal, flats would be better.
Only had to push a few sections because of technicality or grade. mostly the track was rideable in my lowest gear. (rohloff 44-17 at the time) lower gears would have been better though.
I pack lighter now, which would help.
beautiful area. links up w dirt roads periodically between sections too, if you want to have a bit of singletrack and a bit of fire-road stuff.