I should update.
First off, I was wrong about the 7D2 charger not charging the LP E6 batteries. The only batteries it won't charge are my aftermarket Maximal Power batteries. It also turns out I did pick up a used 5D3 from a friend of a Flickr friend. Just under 34,000 actuations and I DID buy the grip as well! (also his mint 500 f4, but that's another story!)
So the charger that came with the 5d3 WILL charge the aftermarket as well. It's likely an older unit than the 7d2 charger, although as Furlan mentioned above, they are all labeled LC-E6, but the newer one has UL Japan and the other 2 say Cosmos. FWIW, the silver box in the bottom right corner reads AEAD on the 5d3, ADAD on the older 7d charger, and CIGD on the newer unit. It could be that other aftermarkets work fine. Also the 5d3 gives the warning message when using the Maximal Power. I only have 2 of those, so maybe they'll just remain on the back end of any rotation.
Thanks for all the helpful input and I hope everybody has a great New Year!