I wrote out a lengthy analysis of the system. I may find mistakes later, but I am taking a break now.
It appears I can remove the ECM from the starting system just by jumping the BY and BW wires at the starting relay. Unless I'm missing something, this should allow normal starting with the key, without harming anything at all. I will keep looking at it. I would still have to use the manual shut-off to stop the engine if the ECM won't do it.
The shut-off relay can be bypassed by jumping the W and RW wires, though, so using the key to shut the mower off is possible.
The key won't give the relays too much juice and damage them. It supplies the relays with juice when the ECM is working, so the relays shouldn't know the difference.
If I am right about this, doing it would be very easy. I could even do it temporarily without cutting into anything.
I am not planning to do it, but it's something to think about if the ECM turns out to be bad. I think it would be pretty simple to add a couple of safety switches (PTO and motion levers) back in if I wanted. I have no warranty to worry about, and the ECM may be unavailable if I need one 15 years from now.
The brake safety seems stupid to me. I see why a seat switch makes sense on a machine with nothing between me and the front of it, but I am supposed to be using the seat belt anyway. The motion lever switches seem like a good idea. I'm not sure what purpose the PTO switch serves except to prevent me from being startled because the blades try to move when I turn the key. Maybe someone here can tell me. Maybe it would harm the mower to start it with the PTO engaged.
The only other thing I know of that the ECM does is keeping the shut-off solenoid going for around 10 seconds, but I honestly believe I can handle that myself, or I can do some research and make a circuit that will do it for $15 instead of $340.