Far be it from me to discourage anyone from seemingly pointless electronics tinkering, but from your description in post #15, I'm almost certain you've got a battery that's on it's way out and the charging system is fine. You could verify this by charging the battery with an external charger, letting it sit for a few days, and then monitoring the voltage across the battery with the starter cranking. You could, of course, build an Arduino based voltmeter to do the monitoring.
It is entirely possible for alternators, rectifiers, and regulators (especially Honda regulators) to fail or display curious intermittent behavior, but if sitting unused for a few days is a necessary part of the failure, it's the battery.
As an aside, if the polarity of a functional alternator were reversed across a functional battery, the relevant thread topic would be Arduino based fire suppression systems.