Unusual situations call for unusual solutions.
Being on-the-move is normal for many; but, most have a 'home base' where some things can be stored. This allows traveling light. You know this.
A snail carries everything in its shell. An equivalent for you might be a large-enough container to hold most everything you may need; but, the down-side is the inconvenience of moving it.
Back in the day, a steamer (travel) trunk was used. While most are like large footlockers, some were vertical with shelves and drawers. They are strong and relatively inexpensive. You could probably get one made or modified to your exact requirements. There are all sorts. You probably wouldn't mind living out of one if it met your requirements. I put one of mine on a small mover's dolly to make it easy to move around and go over door sills, etc. It's not difficult.
They used to carry a traveler's possessions from trains, to hotels, to boats, and back to home again.
If you have your own transportation, you can move your things whenever and wherever you want.
If not, express shipping is inexpensive but slooooow. You might want to split your things into two containers. Keep one and send one ahead to your next destination. When you leave, ship the one you have to catch-up with you at your destination or take it with you. Meanwhile, one will be waiting for you when you arrive. Rinse and Repeat as you go.
(Whew ! - maybe not.)
This should work for you* as it's a tried-and-true solution that has withstood the test of time
*That's until you meet someone who you can't live without and will glue you to a spot— of their choosing— on the planet.