Sorry to hear about the recurring electrial gremlins.
Here's a couple of places and things to check before a more thorough in-depth check is needed. i.e. this is what I would check first if it was mine.
There is a lot more to check than what I'm about to mention, but it's a starting point.
1) Battery terminals clean? On mine, I have to clean them 2-3 times a year because of corrosion. Even though you are hooking up a battery charger and it charges the battery, you could still be having a poor connection.
2) Check Battery electrolyte level in each cell. Even with a newer battery, this could still be an issue. I had low levels occasionally. I would re-fill cells and charge the battery. Battery showed proper charge level at first then die out. Over time it worsened and the culprit ended up being a bad battery. And the battery was only a year or two old.
3) Check voltage. If you have a voltmeter or multimeter, check voltage on the battery terminals both prior to starting and after it's running. Voltage should be over 13 when running. If your not getting 13v at battery terminals, then place voltmeter leads into the wires leading to the terminals. If your getting at least 13v, it's charging but the battery isn't taking or holding the charge.
These basic checks can rule in or out the battery and/or terminals.
If all above is ok, with the history of faulty wiring, you could then start tracing bad wiring by conducting ohms checks at point A and B of a particular wire.
These are some of the things I would start with prior to checking the more in-depth items, (battery load test, stator, rectifier/regulator).
Again, I can offer help if you want and check things out for you.