I think I have a partial fix to this. I had exactly these problems with the aircraft I use most: Cessna 172 G1000 and Caranedo Cessna 182 RG II. I also lost all avionics shortly after the flight started. Sadly, I can’t get the flaps on the steam gauge Cessna 172 to work.
Peripherals (like my Thrustmaster Airbus TCA Throttle Quadrant that I use for all aircraft) get automatically entered into the devices list under Controls. They inherit lots of complex bindings. It is conflicts from these that are causing my avionics and flaps issues.
To resolve it, I started with a clean (i.e. empty of bindings) profile. Under the Airplanes Controls, duplicate the none (i.e. all empty) profile to a new one (e.g. I call mine GA TCA Throttle from scratch) and start putting just the wanted bindings in to this. Use the built-in profile as a reference source if you’re not sure how to bind a particular button or lever. Be sure to get things like input repetition, set inverted axis, set control on release correct.
Test the new bindings. For me, the flaps now work correctly as do the avionics. I hope this works for you too. If it does, you might want to copy the profile to other (or all) aircraft.