If it were a stock wiring system, it would be much easier to trouble shoot than with an M-unit thrown into the mix. If you had a short, with a stock system you would blow a fuse, but the M-unit has built-in breakers that reset. Right now, it sounds like your issue isn't a charging fault, but an excessive load, brought on by pressing the start button. Why the load doesn't go away when the button is released, but does after the key is turned off, is a mystery....
For now, don't even try the starter button at all, and see how the charging system works.