Just returned from a pleasant trip on the Dirty Devil in UT. We opted for a relatively unusual shuttle option for the lower 48: small plane. There is a strip at Hite, at the confluence of the Dirty Devil and the Colorado, and several backcountry strips upstream including one in the DD canyon across from Burr Point and one at Angel Point near the head of SF Robbers Roost canyon.
The river is mostly flatwater, but the canyon scenery and side hikes are outstanding. Much less floater/hiker traffic than over on the Escalante.
Park your car at the Hite airfield, get picked up and dropped at the upstream landing of your choice, then float back to the car.
Nick Lamoureux at Redtail Aviation (in Moab) can hook you up.