Can I use SCRs as the uppers in an H-bridge?
A reason SCRs aren't used for push-pull schemes involving high frequencies, as far as I am aware is the abominable turn-off time of the things.

Gate trigger to conductance can be in the micro-second range for most types, but for many types that I am aware of turn off times are in the 10 to 100us range, which is pretty much the death of any efficient use of a square wave or PWM signal for power conversion.

There may be whole series of SCRs that are super fast in both regards, but I haven't heard of them.

EDIT: (In SCR's turn-off time is not the transition of stopping to conduct, which would not make much sense anyway, but the time the device is expected to be "relaxed" before a voltage is again applied that might induce current over its holding current. This is the time needed for the blocking diode barrier to regain its withstand voltage. So some tweaking may be possible by using an SCR rated for 200V at 40V, but it won't be an order of magnitude.)