He confirmed the MD22P is isolated when the starter and stop solenoid aren't working, and connected to both plus and minus momentarily when they are activated. One thing I forgot when I wrote the post above was that I had also connected a new hour meter at the pedestal. He suspects the way I wired it I'm back-feeding the ground of the instrument circuit, and the relay is causing a transient spike. (The way I wired it was that I tapped the hot lead from the tachometer, and connected a ground lead from a nearby wire of unknown origin that was mysteriously unconnected but available inside the pedestal.) He also told me how to wire the hour meter "properly"; where to pick up power and ground so that it won't run unless the alternator is running. (BTW he's also puzzled why the stop solenoid would spike it but the starter doesn't.)

I'm going to re-wire the hour meter next time I can get to the boat and see if that solves the problem. If not, next step is Raymarine tech support to find out more about what that fuse carries the load for.