Welp, I found a way to at least get around the spam until the issue is fixed. I know this a far-from-ideal coarse workaround (or a blunt hack if you like), but at the very least we can continue to play in peace, though not with active ground science transmission.

In the persistent.sfs, changing ALL instances of the lines:

name = ModuleGroundExpControl

isEnabled = True

to

name = ModuleGroundExpControl

isEnabled = False

(or just turning off the ground science controllers in-game) will stop the experiments from communicating in any way, thus eliminating the message spam but also all associated science. Reversing the operation (in-game will take a kerbal physically at the experiments, which defeats the purpose) in Notepad will turn them back on.

Disabling the ground communicator in the same way didn't seem to have any effect (at all? I know I tried it but I don't think the ground comms have the same mechanics as the experiment controls, and I think I saw that when a ground controller has a nearby antenna, it changes its own comms power, so...).

To the best of my understanding, there's nothing that changed in the .sfs that would cause this, and my own and rrowland's experimentation shows that newly deployed modules react with the same bug, in old saves or new (I checked).

Please make no mistake: I do not consider this to be any kind of acceptable fix. This is a simple hack to allow play until the bug is addressed in a patch.