This sounds like a great plan to me! This is very close to what we are currently doing.
Don't worry about the permanent address. Either use your son's - or if you want to use a state that has no state income tax - you can do that, too. We have used a place in Pensacola, Florida. Military people and people who are full-time RVers do it all the time. You are set up with a street address and mail forwarding.
Don't be swayed by those who aren't adventurous enough to try. I say GO FOR IT! And enjoy!