Here's a somewhat simpler approach that may work for you as well.
I found, that once I got the back off, the charger seemed to work better. I think, with the back off it gave the frame a little more flexibility, and allowed me to push the USB charger in a little tighter and make better contact. That told me, that the internal mirco USB port and cable were OK, but just not making good contact with my charger.
So, I sealed up the tablet, and using a sharp knife, I shaved a bit of the rubber insulation off the end of my USB charger. That allowed for more of the metal end to stick out and make better contact.
For the moment, it seems to be working, and saves mucking around with the inside of the tablet.