The key observation is that both engines misbehaved in the same way, when you installed them on that mower. The next step should be to put a voltmeter on the kill-wire running to the mower (with it disconnected from the engine of course) and switch the engine on and off at the engine stop switch on the mower. See if 12 Volts appears when switched on, and disappears when switched off. If it does, it may be curtains for the ignition modules on both engines. Is it possible to try both engines on your other mower? If you do that, we'll have some very clear evidence.
I don't know how long it takes to destroy the module if you put 12 Volts on the kill wire, Paul. We've had several cases where the presence of the 12 Volts was only discovered after the module failed.
