We really need to get you a scope of some kind. A $7 USB sound card and a DIY interface goes a long way.
http://www.electronicsfaq.com/2010/05/poor-students-oscilloscope.html is a good reference. I suggest the CM108 chip set. Also good reference
http://www.automata.hk/projects/scope this interface is a bit better
http://xoscope.sourceforge.net/hardware/pictures.html and the USB sound card found here
http://www.ebay.com/itm/Audio-Sound-5-1CH-Blue-Card-External-Adapter-USB-2-0-to-Mic-3D-New-Speaker-E456-/271265265387?pt=US_Sound_Card_External&hash=item3f28ab76eb
Any how, that said, the high voltage GND loop is much smaller and the voltage drops from the spark currents shouldn't be pulling the STM GND up any more. Well at least from a DC standpoint. Assuming the issue is still a bad GND, you can try taking that wire between the battery - and the coil and wrap it around a nail or some kind of small iron object, or if that's hard to find pencil or something would be better than nothing. The goal is to make that GND wire into a kind of small coil. Coils don't like to change current, and such a small coil will help choke off RF from the coil potentially preventing RF from spreading to other things on the wire. I'm a skeptic it will help significantly, but eh, won't hurt, so might as well try it. I'm also assuming you don't have an RF choke similar to this.
https://www.google.com/search?sourceid=chrome&client=ubuntu&channel=cs&ie=UTF-8&q=ferrite+bead#channel=cs&q=ferrite+bead&tbm=shop
There is still a chance the issue is a bad GND, especially when I don't know the tech inside the coil on plug. Is that an OVP MOSFET, IGBT with snubbing diode, ect. I'm basically guessing at large portions of the circuit. My next guess would be that it's not the GND. If there is some kind of spike, that could be coming back up the low voltage signal wire. Perhaps add a diode in series with that signal wire to help block that kind of kick back from making it back to the STM. I guess also try the same for the 12V supply. But try it on the signal wire first. The goal is to only allow current to flow one way, and prevent current from flowing the other way.
Also how is the STM powered? Do you have a 5V regulator that's powered off the battery - terminal? I see both USB ports, I wonder if the PC might be floating relative to the battery. All you need to create an issue is for the STM to lift by like 1 to 2V, or for the rail voltage to drop 2 to 3 V for a short period of time.
If you had a scope, you could look for GND issues by connecting the scope GND to the battery terminal, then use the other scope lead to check various GND points. I wonder if a multimeter might help. Most multimeters are for very low frequencies so I would expect it would not detect such a short pulse. However it might be worth a try. Couldn't hurt. Using the MAX setting can often catch a short term pulse, but often it does not.