Okay, I just stumbled across a workaround for this issue that actually works, and doesn't require any jumping jacks or hokey pokey with device unplugging. Just a little bit of thoughtful trial and error.
Basically, editing the configuration file :-)
So basically make a copy of your configuration file:
(in my case, having installed via Steam, this is where it is)
C:\Users\myname\Documents\STAR WARS Squadrons Steam\settings\ProfileOptions_profile_synced
Then go into the game, and mess around with the particular bindings you're trying to change. Each time you change them, compare the updated file to your saved copy. It shouldn't take long to figure out which key corresponds to the setting in question. A little bit of trial-and-error from there, and you can find the identifier for the axis direction the game won't let you bind.
In my case, I was trying to bind yaw left/right to my Saitek Pro Flight Combat pedals. In the game, these are joystick 3 (a.k.a. device 2 in the config file)
The corresponding settings keys were "ConceptYaw.6" (right) and "ConceptYaw.7" (left).
Binding the "yaw left" direction was do-able in game, and set the following lines:
GstKeyBinding.IncomStarshipInputConcepts.ConceptYaw.7.button 47
GstKeyBinding.IncomStarshipInputConcepts.ConceptYaw.7.deviceid 2
Binding the "yaw right" direction required manually editing the configuration file to set the following lines:
GstKeyBinding.IncomStarshipInputConcepts.ConceptYaw.6.button 46
GstKeyBinding.IncomStarshipInputConcepts.ConceptYaw.6.deviceid 2
Once I saved the changes, I restarted the game, and both yaw directions were bound correctly! (and yes, they both worked)
In other words, the bug that's driving us up the wall is in the settings screen, not the game itself.