You sound like you know what you're doing, so pardon me for this stupid question....What are you using for a spark plug? It's not some weird one with an extra internal gap for "more power," is it?
Maybe your flywheel was replaced at some point, with the wrong one....
If it were me, and I got a fourth module, I would probably close the plug gap down to .020" inch and see how that worked out. It might foul too fast or it may make it a little easier on the module....Just an idea.
An R7070 is a cool mower, worth the extra effort!