Hi David -- I recall your purchase, proposed relocation, and
even the barging to the current location. Your story moves along...
The tires are toast. I've got 1 1/2 tires on my Argosy that behave like that. I'd probably move on to your proposed solid support underneath. I sure wouldn't buy new tires to sit in the sun for years and be bad news when your grandkids decide to go caravanning ...
The strong axle mounting plates and the ball (A-frame) are the only areas built to carry load in the long term. The frame should not be set up to hold weight at the corners -- the frame will bend, skin might crinkle, the door won't open (or close); the corner location of B.A.L. jack stabilizers is only to prevent shaking of the trailer as you walk around. If you see any "jack point" decals underneath, they should receive no stress beyond what stabilizers would apply.
You probably wouldn't want to use simple cinder blocks -- it sure's not safe to work under a car on cinder blocks. I'd probably build some timber bunks. It's a good thing that you won't have to deal with ground frost.