@Gobokat and @mistyty@mistyty, The construction of the ramp may not be your problem - if I'm understanding you correctly this "wagon" is 72" long, and have a 3/4 ply base. Is that what your casters will be bolted to? What I'm asking is what is the clearance between the bottom of the wagon's deck plywood and the floor. You need to be sure that as your 72" long board travels over the ramp (i.e. the dropping away floor) that the deck won't catch at the transition from the plane of the platform to the ramp.
You can add more wheels so that it stays level (going down) or inclined (going up) until most of the wagon has transitioned and then it will tip to the 'correct' orientation. Off-hand, unless I would say that a set of wheels every 2 feet along the direction of travel on the ramp would do the trick.
Also - you were saying that the wagons are 72" inches square, but your ramp is 4 feet wide? so I am guessing that there is not enough weight on the part of the wagon that won't be riding on the ramp to cause it to tip?
'way back there somewhere, I believe Ms. Misty mentioned her scenic flats were ~6' tall by ~6' wide. I don't recall any specific thickness being posted.
I suspect what Ms. Misty has in mind is a ~6' tall by ~6' wide flat rotating parallel to the ramp and being rolled up and / or down the centre of the ramps with ~18" clear on either side to walk on. I could easily be misinterpreting this; I've serious vision impairments with senility settling in; I could very easily be incorrect. I've decades of experience at being incorrect. Fortunately, I've learned from all my errors, remember what I learned, and I've chalked them up as experience.
You're entitled to your wrong opinions, as am I.