For on-off keying of a switch mode PA you really should be using supply line control. Switching the drive then trying to reduce rise /fall times for keyclick elimination by controlling drive amplitude(something that seems to be done in some designs) is really asking for trouble. Even hard-switching drive gives its problems , as we see here repeatedly
Instead, why not a simple emitter follower in the positive supply, then you can apply waveform shaping to the base drive at low current, where you've got full control. Even a 20A supply could be controlled this way with a suitably rated transistor. Quite likely have to be a Darlington. There will be a slight fixed drop across it, say 1V at saturation / full power, so a few watts of dissipation, but it's only operating non saturated for a short period during the rise / fall times.
A power FET could be used, but you'd need a drive voltage Vgs higher than the supply, albeit only a few mA capability; nothing a small switcher module couldn't manage.
