Mac will only charge if entirely dead or using an unofficial charger

The Macbook communicates with the charger via a communication protocol known as "1 Wire" which is used in some Maxim semiconductor products. If you look at the MagSafe or MagSafe2 connector, you'll see it has 5 pins. The two outermost pins are GROUND, the next set of two pins are + POWER, and the center pin is SENSE. The SENSE pin is allows communication between the MacBook and the Charger. The charger implements this communication with a Maxim DS2413 chip in the charger which returns a 64 bit identifier to the MacBook. This ID is used to identify the charger model, wattage, serial number, and charging status. The MacBook can both read this ID and write to the DS2413 to control the multicolor LED in the MagSafe plug. There is a good writeup of the process in Ken Schirriff's blog at: http://www.righto.com/2013/06/teardown-a... as to how this works.

I suspect that the reverse polarity damaged the circuitry that controls the charger-to-MacBook communications on the MacBook side. My guess is that Apple does not interrogate aftermarket chargers in the same way it does it's own - that is, it just gives them a pass. That would explan why the aftermarket charger works. A communication failure would also explain why the Apple charger only works when the MacBook is completely dead and thus would normally be unable to communicate with the charger. Hopefully Ken's article will help you toward a solution. Finally, if you have access to a logic analyzer (or even a scope) it would probably be worth a look at that SENSE pin, or maybe you can trace it on the MacBook side.