You would want the tire beads to be able to "crush" a little bit in order to seal.
Instead of steel, I've got a buddy who just ordered a strip of UHMW plastic (like 1"x1" square x 60" long per rim). The plastic is relatively hard but is still flexible enough to bend it into an "O" shape. Since it's sort of "spring loaded" when rolled, it springs open against the beadlock bolts.. holding itself in place.
The stuff can also be cut/sanded/ground down to a whatever thickness you need.
I would probably mock up one of the tires, lightly snug the outer ring in place, measure the gap between inner/outer rings, and then pick the thickness that's the same (or slightly less than) as that. If you've got access to a table saw, planer, bandsaw..etc, it would be really easy to trim down the strips to allow a good clamping of the bead without coning the outer ring in.
Part #8702K122 at www.mcmaster.com