I have a tyre-carying frame on the front of my trailer .... you can see it at
Lay Flat Trailers - Australia?s first and only trailer that can be lowered completely flat to the ground
Let the gallery shots cycle thru until you see trailer plate number T59-179 ... the tyres "sit" on the lower part of the frame at the front (you lift the upper frame out of the way, put the tyres onto the lower frame and then lower the upper frame and lock into place).
I prefer to have the tie-down mechanism on the tyre rubber rather than thru the centre bore of the wheel itself.
I'm assuming your "tyre-trailer" is just for tyres and gear rather than carrying the car as well, but if you "get" the idea, you can fabricate a lightweight frame (or cage) to go over the tyres like I have on my trailer - it only needs to be a pair of parallel tubes or perhaps RHS steel, joined at the outer ends, with the tubes ~40-50% of overall tyre diameter. You can then secure this with a pair of 1" ratchet tie-downs.
RB