The other challenge is pushing the coolant through the coil!
Back when I was doing electromagnetic levitation/containerless processing at Rice, I was trying to keep cold from melting down with a kilo Amp of 40 kHz RF going through them. I had a serious pump and found that 3/16" was the smallest I could use without making steam. Skinny tubing = induction awesomeness... I did some stuff with rectangular tubing also, but it really didn't play well with the funny shapes I needed.
So, for your stuff, some suggestions:
Hook it up to compressed air and a muffler. Put the throttling valve on the outlet: heat transfer is related to density, and compressed air is more dense.
Hook it up to city water with a long coiled hose to keep the RF out of the pipes.
Make a pressurized water reservoir and pump it up before a heat cycle.
Find a higher presdure pump. A tiny/cheap/Harbor Fright pressure washer pump isn't insane for this.
Consider larger diameter tubing squashed oval after winding. Ideally squashed while filled with something like low melting metal. Also consider installing thin insulation on the coil to allow the turns to be closer together.
Fyi, theres going to be an optimum inductance, if you start changing the coil. Lower inductance = more current = more heating = higher capacitor current. The caps are probably your limiting factor!
Sent from my SM-G892A using Tapatalk