One possibility is to hand select and pre-kit a set of Ls and Cs that hit the frequency. That's inelegant, but I could have an intern spend a day selecting a lifetime supply... we'll probably only build 10 or 20 systems ever.
The drive is: +30 DC on one end of the tank. One the other end has 100 ohms to the drain of a mosfet. The source is grounded and the gate is pulsed at 107 KHz,
25% duty cycle. So we get 60 volts p-p across the tank. It's sort of like a class-C RF amp. We want peak amplitude and minimum phase shift. These are all system specs, not mine.Whatever tuning mechanism I find, I have to tune it. The peak amplitude point will be hard to find. Maybe I can use a DDS to tweak the frequency and find the two -3 dB points, which would be more sensitive than looking for the peak.
That inductor would need a big percentage tuning range. Messy math.
I sort of hate inductors. They are the least ideal, least accurate, hardest to measure, hardest to buy parts. Somebody could set up a garage shop custom inductor business, especially stuff like tunable pot cores, and do OK.