I did just that, but the hardening "broke" the easy oscillator, which was touchy to make happen as it was. I can only assume reduced parasitic inductance caused that change.
Rather than fool around endlessly with coil turns ratios and so on, I decided to take some measurements on transit times and phase during changes and just drive the thing.
Now, I may go back to square one, you never know, but since it's kinda hard to "tune" that stuff remotely, it would involve endless back and forthing to tear off the EMI shield, change something, put it back, run the checklist again at the remote position...repeat.
I know some rather surprising things I didn't know before as a result, but only time will tell how things end up, eh?
I did find something new but obvious in hindsight. At the pressures we're running, with the current ion source (which I like the best of all tried) we are not seeing a lot of space charge effect out in the bulk tank. We do start seeing it late in a driven "cycle" when they're all close to the grid instead of spread out all over. We also saw that with effective pressure in the sense of molecular vs viscous flow in some earlier experiments, so in hindsight...duh. But in some ways this simplifies a lot of math, and also tells me some things that weren't directly easy to measure. So good.