I don't see the reason why this should not work but let me give you an alternative.
It might be even cheaper (especially while you're still in the designing phase of the PCB) to design better cooling for the chip.
Use of large ground layers and thermal vias can help with heatsinking enough to cool the chip.
There are even some SMD heatsinks (although they are usually a bit expensive), but you can design the PCB such a way that a normal heatsink can be pressed against the chip (with screws for example). With a bit of thermal paste, this should work well and since you're on a budget, save you a bit of money.

You could also parallel 2 chips and use one GDT.

The best running PLL coil I've seen is the already mentioned Jakub Tejiščák's coil, although I've never quite understood how does his approach achieve ZCS:
https://www.vn-experimenty.eu/teslov-transformator/sstc/sstc-5.html
He is modifying the value of R2 to get ZCS, but in my understanding, R2 is there only to set the frequency range at which the PLL can operate. Somehow it works though. Maybe someone can clear this up?