I think the set up you describe would be less reliable then using PWM output, with a raspberry pi in the equation. I think you'd be better to use an SSVR and rig up a digital potentiometer to the pi, these work via phase angle.
My first time seeing the name SSVR, but from few minutes of googling it looks like that's what I have (just built from discreet components). That's a good idea about using a digital pot, that hadn't occurred to me before. It would definitely simplify things for me.
The time response in the RPi OS will lag too mutch for a application like that. I would resort to an Arduino doing the timing and communicating with the Pi via serial or PWM.
Seems like you're in agreement. So I gather that I might have overestimated the Pi's GPIO capabilities? I haven't really looked at the specs at any length.
Although the real time response isn't really all that important. Just so long as the ON pulses fire at 60Hz and there's a timer that can measure delay, it doesn't really matter if there's a delay of a few cycles between the input trigger and the output.
Maybe I'm misunderstanding the constraint?