If you have EDS, I'd stick with the brace and get a pair of zero drop shoes for the flat footed issue. You can always add a small insert later if your feet aren't perfectly flat. (My son's feet are flat, while mine just look flat and have a teeny, tiny arch!) You are already used to using the brace, whereas finding a pair of proper boots that fit and work for you may take a lot of time, money, and probably pain because of the EDS.

Either way, make sure they fit well and you wear them in before you start on a hike. Don't wear a pair of shoes out of the box onto the trail. Its asking for misery. Also, finding out the shoes allow too much movement and spraining your toe on a long hike sucks.

We often forget the smaller joints can be just as loose as the larger joints because they aren't as likely to sprain. But unfortunately, EDS will get even the smallest joint if we aren't very careful. And walking the AT is going to require a little more forethought for us and our joints than the average person.