Hi!

But this is one of those "fully electronic" disasters with touch pad
controls. And, in theory, an electronic hygrometer of some sort that is
supposed to control the whole process.

Ever thought of bypassing this to see what happens? It shouldn't be too hard
to disconnect fan and compressor, after which you can power them externally.
You might even be able to hot-wire the unit and get an external humidistat
that's capable of turning it on and off at the prescribed humidity level.
Make notes, drawings or take pictures of how it all went together. It is
most likely a bunch of spade lug connectors that plug into the control
panel.

You might even be able to get a good humidistat from an older unit that has
had another failure and wire that up.

A compressor that's "banging away" is either in very poor health (!!!) or is
being abusively cycled on and off. If the fault is really in the compressor,
you probably cannot do very much about it. If the fault is in the
controller, I'd be *very* tempted to wire around it and use the unit that
way.

William