Understanding certain relationship in Induction heating circuits
Induction heating is not a resonance phenomenon. There is no one resonance frequency that will work better than any other. Rather, there is possibly an increase in magnetic coupling efficiency with increase in frequency, then a decrease with further increase of frequency as losses (skin effect, capacitive interwinding coupling, etc.) increase.

The major factors in how fast you will heat is the geometry of your magnetic system, the amount of current you input, and the magnetic coupling coefficient (which is frequency-dependent). 

The geometry will influence the efficiency of magnetic coupling to the specific shape of object you're heating. 

The eddy current induction in the object being heated is strongly dependent on the current in the induction coil. So if you have a coil with many turns, the effective current is multiplied, very much like the turns on a transformer winding. For maximum induction efficiency, you need to match the inductance of the induction coil to the electrical drive. Vdrive= 2πfLI. In an induction coil with few turns and no ferrite you will have small L, consequently I can be large for a small V.

If you are limited to the existing power supplies you have, then the major factor you can control is the number of turns of wire in your induction coil, and the core material. I would start out actually measuring your coil voltage and current under operation. It's possible that your power supply is poorly matched, and is actually current-limiting so that you are not supplying nearly as much power to the induction coil as the power supply is capable of delivering. In this case, increasing the number of turns in the coil will make a big difference in heating efficiency.