I'm not an user of SG II as you know but I have some experience with electronics. Recently I was "fighting" the issue with MPGuino after installing of kill switch. Killing the engine by cutting off the solenoid was causing electric noise which was messing up with guino. The same issue was during starting the engine. So I needed to cut the noise.
First I've mounted a noise filter on the cable providing power to MPGuino and then diodes on the kill and start switch to cut the voltage pikes.
Cutting the noise from a kill switch
It's working very well right now and I can stop and start the engine without any effect on MPGuino.
So first of all maybe you should check if there are any voltage pikes or other noise during killing and starting the engine again. Then it should be fairy simple to cut the noise.
One more question - SGII is acting weird when you're killing the engine or during restarting it? If when you're restarting the engine let me know if that is when you're using starter or bump starts too.