annual inspections & registration on extended trips

For Texas, if you're out of state you can do it all online and just check the box to let them know you're out of state. No inspections are needed unless you come back to the state. Then you have three days to get it inspected. If you're just driving through and you can make the drive in 3 days (it's a BIG state), then just drive on through and no inspection is needed. It's simple.

Most full-timers have sold their house so they don't have a 'home base'. Their RV is their home and they're always home.