What about this solution--
a fore-aft accelerometer (or a set of accelerometers) which actuates the standby mode. A single fore-aft acceleration beyond, say 100 mm/sec^2 (0.01 g) would cause this to shutoff. My logic for this is the following--in order to drive the car, there must initially be some non-trivial fore-aft acceleration. When the instrument feels that the car is starting to move, then it will shutoff the device. Don't worry about average 'drive' accelerations, just worry about the initial acceleration that the undergoes when it starts to drive.
Three potential issues which I already see, but which may not be a big deal for you:
1) Is the damage already done once that initial acceleration occurs?
2) This presumes that the fore-aft driving acceleration is sufficiently higher than your machine's general in-use acceleration environment. I presume this to be true based on your discussion, but that is yours to confirm.
3) Your initial statement was that you wanted to detect the fact that the engine is running. You have since stated that the concern is actually the car in motion. This proposed solution focuses on the car in motion. This would not turn off the car for the non-moving engine running situation.
And Greg, throw in your input on my solution. I think it holds water, but if I've overlooked something, I'm quite sure that you'll pick up on it (and I mean that as a sincere compliment).
Brad