Back in industry, I used a single stage, full wave, frequency offset control. Simplest power stage, but crappy to compensate. Wanted to try phase control, but the driver and output stage didn't have the logic to support it. Yes, you need a PLL to track resonance, or something near it in any case. Phase shift PWM gives you effectively a variable voltage source, exactly what you need. With the system at resonance, the amplitude response is a (single or repeated?) pole at the tank time constant, low Q and easy to compensate.
Downside is 100% switching loss and EMI. A tri-level inverter (a half bridge with a shorting-to-zero mode) might be preferable for this reason.
Tim