
Here it is nestled in its home. You might note that the solenoid is loose; this is a 3727 keyboard, which don't come with solenoids. I stole the solenoid out of my 5251 (which lives at home), and left it sitting loose. And here is the fix (note green wire): Basically this hack implements a (crude!) switch-mode current limiter

The wire goes between the enable to the boost converter (bottom left), and the active-low fault output of the current limiter.
The boost converter's enable pin used to be connected to 5V all the time, so it was always powered.
Now what happens, is the current limit is hit, the fault output is pulled low 20-30ms later, which turns off the boost converter. The current of course drops instantly, and 20-30ms later the fault output idles high again, turning the boost converter back on. The cycle will then repeat indefinitely, as long as you still try to hold the solenoid in. Let go of the solenoid, and everything goes back to normal. Not even a little bit of heat! Runs cool as a cucumber.
Here is the fault output cycling while I press a key (then release it): And here is the 9V, which drops down to roughly 5V while the solenoid is held in, and sits there cycling between 5V and 7V or so before I release the key and it charges back up again: I need to polish off the firmware a bit more to properly test it (it's only firing off the LShift key at the moment as a quick hack); hopefully it'll hold up under fast typing. But looking good so far.