This is a problem that has exercised my mind while waiting for the assemblage to tune up (I have already achieved perfect pitch).

My take was to cut a hardboard or plywood round to cover the skinand maybe some form of foam edging to keep it in the safe zone and cushion the edges. It would fit inside the case and stuff underwear &/or jumpers in the void to pad the open end. The frame would be strong enough for most purposes but a circumferencial foam strip might add protection and keep the whole thing taut.

I took the bar out of one and put the smaller on inside and carried the lot as hand luggage. If you don't have any other hand luggage you might get away with it. There is room in there for emergency underwear, first aid, camera, sweets. It all depends on size and regs.