Don't understand why you keep going back to center tapped work coils. Almost all industrial induction heaters and the ones sold for hobby use use single coils not center tapped.
If you do some research on the zero cross style modules and buy a good one, not the cheapest one you can find, they do work. There's a guy on Youtube that spent the time and money to test them and found one that does work.
Instead of beating a dead horse spend some time on research.