Just dont see how these would help stabilize. You will lose the tire bounce but the springs are still going to move. I have a large dog that can get a trailer bouncing pretty good when he plays so I have an extra set of scissors jacks that put under the center of the trailer on the frame right in front of the front axle that takes a lot of that bounce out.
As far a long term storage goes just keep the tires out of dirt with a 2X12 under them and cover them for sun damage. Radial tires can sit for a long time and any flat spots will work they way out very quick as they warm up.