It has been a while since we made any progress on this so I ran a rather unscientific test and found something that may or may not be significant.
I was looking at some posts in the
Canon EF lens mount - Communication protocol topic and one of the links pointed to an interesting experiment to control the lens using an
Arduino board. This particular suggestion to throw out cable that connects to the image stabilization system was intriguing:

Not wanting to take apart my lenses and start cutting cables I thought an interesting experiment would be to block each pin on the lens to see if perhaps one will have an affect on the shutter-bug. Yeah, I know the lens/body communication is more complicated than that but as a kid I used to stick various objects in to electrical outlets to see what happens so I thought, why not?
First problem was that I couldn't find a pin out chart for EF-M lenses. The EF to EF-M adapter is wired one-to-one but there are 8 pins on the EF, EF-S side and 9 pins on the EF-M side. Note that two pins are used for P-Gnd on EF lenses but apparently this is different on the EF-M so there
might be two pins that are used exclusively in the EF-M lens protocol.

What I did was to use a small piece of tape to block one pin at a time and eventually I found something that eliminated the shutter-bug. Well, sort of. Blocking the pin that is probably the +6 volts to power internal lens focus motors with the lens in manual still photo mode, the shutter-bug disappeared. Of course this isn't a practical solution, the lens isn't getting power so the aperture is stopped down all the way. However, I was able to shoot stills with no sign of the shutter-bug. Now for the weird part, with the camera on full auto mode, the shutter-bug is present. Not only is it present, but the workarounds we use to kill the bug don't work.
If we call that "VBat" pin #1 (if indeed that's what it is on the EOSM) then going through the other pins and blocking them created some interesting results. First of all, the next two pins should be power ground and blocking one should do nothing but on the EOSM I got different results blocking each pin.
Blocking pin #2 caused this error:

and saved
this error log using the lua_fix branch.
However, blocking pin #3 caused this error:

and
this error log. So obviously these aren't the same as the EF/EF-S pins.
Blocking pin #4 the camera wouldn't even start.
Blocking pin #5 gave Err 01 and
this error log.
Blocking pin #6 gave Err 01 and
this error log.
Blocking pin #7 gave Err 01 and
this error log.
Blocking pin #8 did nothing as far as I could see, no error message or log and the shutter-bug showed up as expected. Maybe it isn't used on the lens I used for this test?
Blocking pin #9 gave Err 01 and
this error log.
This test was done with an 11-22mm EF-M lens and a 64GB Komputerbay card that reliably shows the shutter-bug.