How can I get my flavorings to flavor my carnitas all the way through the pork?
One of your possible answers is pretty close to what I think is the correct one. To flavor carnitas all the way through, put them back in the braising liquid that has been reduced since cooking the pork. You can create a kind of glaze out of the braising liquid, and toss the shredded pork in that (defat the braising liquid before reducing it).

BTW, I never fry carnitas. I may throw them on a greased grill, but I never deep or shallow fry them.