BMX pro tires might work well for you. They are made to jump and bang on steep corners and metal ramps. $38
24x2.0 wheelchair (offroad) tires $17
They might be kind of soft (so they don't scratch floors), but they probably have good quality beads and molding. Might be worth a try.
24" tires have a 507mm bead seat diameter, if that helps you search.