We camped every night expect for the two nights in Portland and it was very easy to find BLM or National Forest land for free camping. It is amazing with not much planning, you can find plenty of sweet campsites along the TAT. We literally pointed to a flat and nice spot every night and said, "Here looks great." The TAT borders and goes through public land, so obviously this helps. However, we took highways and interstates back to CO. We found plenty of free camping spots with no more than a 15 mile detour. It helps if your GPS indicates public land from private. We spent under $50 on camping at 2 campsites for two weeks of travel. One was forced as you saw we stayed at the Black Canyon due to a mechanical and the other one was at a State Park in ID as we just finished a 500 + mile day and saw the spot off of the Interstate.
Camping helped us to connect to the utter remoteness of the TAT. I highly recommend it!