Non-linear springs, yes.
Headache to set up, yes.
Gyroscopic forces, yes.
Would it be worth it, not sure.
non-linear springs is a non-issue. Almost all commonly available springs have the spring rate rated in force per unit of travel and they're progressive.
gyroscopic forces on a generator rotor are a non-issue. Those forces are so small compared to the attraction force between the rotors that they are negligible.
After reading your post this morning, and reading Flux's post I suddenly had a wild idea and this is something that even I would try. As Flux noted, a three-step system would be better than a two-step star/delta switch.
There is a situation where you need a tighter air gap at high speed than you need at low speed. That situation is where you built a generator with the proper number of windings in it for delta. This thing won't cut in until the wind is blowing at 10-12 mph so you start it up in star. But in star the rotor runs so badly stalled right from cut-in that it really doesn't do anything until it gets switched over to delta. This is pretty much the situation with my latest 10 foot test machine.
So what you do is widen the air gap at low speeds in star to let it spin to a higher wind speed - say in the 15 mph range or so - before switching it to delta. But have the governor on the movable rotor start tightening the air gap at around 12 mph so when it switches to delta the transition is less drastic. As the speed comes up after the switch, the governor would move the air gap to its tightest point, which it needs in delta to really perform.
I have a propensity for trying stupid stuff like this and this is not really all that complicated. I'd have to work out the exact details on paper to arrive at what speed the generator needs to be operating at at the various air gap settings, and I have most of the bench test data on my test machine to do that.
Thanks for the post on your idea - now you gave me one and I won't be able to stop thinking about it until I try it.
--
Chris