Yes your understanding is excellent.
The best way to overcome this problem is to make the main high power resonant LCR circuit part of a big very high power oscillator.
The drive power into the tuned circuit is then always in the correct phase relationship, because the drive frequency actually fed back from the output tuned circuit.
When you insert a metal load into your induction heater, the frequency will certainly change, but the circuit continues to drive power into the resonant circuit always with the correct frequency and phase relationship.
This way, the circuit self adjusts in frequency to always operate exactly at resonance, where the efficiency and energy coupling is at maximum.