I’m with
@augiedoggy. What’s the goal? For me, using standard SSR’s with short cycle times (~1 sec) work fine for reasonable cost and installation trouble. You can use a zero-cross SSR if you want to ensure the switch occurs at the base of the AC sine wave. Or use a proportional SSR. These are accessible, low cost, and proven reliable solutions. We are heating liquid, not modulating high speed control systems.
If defined control to the specific AC cycle is your goal, then this is really an academic exercise, upon which the above or other are possible solutions.