Third if you are seeing a 10 amp average current drain the switching devices themselves may be seeing 3 - 5 times that peak currents as well.
If it was me I would be tempted to try and redesign the circuit initially into a H bridge with low ESR capacitors making up one half of it and your switching devices making the other.
Once you have the bugs out of that then I would change the capacitor side of the H bridge over to switching devices and run the induction coil in series with the two capacitors paralleled with each other that made up the second side of the H bridge.
That's basically how most of the large induction heater units are configured.
That's my thoughts anyway.
(But I did just roll out of bed too.
)