For wifi control, just wire a receiver to the input of a solid-state relay.
solid-state relays rated 600VDC+ is pretty common, current can be 100's of amps. Main issue is that SSR rated 600VDC has ~1.2VDC voltage drop.
20kA for 1-10ms is feasible, just crazily expensive. To actually reduce inrush with FETS you can try to use their ohmic property. It's extreme risk, and I would only try it with an unlimited budget lol.