Now that I really look at the layout, having the TV over the fireplace is even worse than most cases. Where are you going to sit? At the dining table. The logical location for seating is at the opposite end of the room.
Is Rube Goldberg still a member here? He always had good ideas for this kind of setup.
Seriously though Brandon, in the quest to make the system simple, you're trying to make it ten times more complicated. Not to mention, most of what you're proposing doesn't even exist, can't be used the way...
Remember, you can always put connectors in place of those little speakers and use floorstanding or bookshelf speakers on stands or small shelves in place of what's there. They don't have to be mounted on the wall.
Those appear to be really cheap, full-range speakers. I'm not sure it's worth bothering with them, but you have them if there's no options. You can use the wiring for better speakers, except the one surround speaker we can see is almost at floor level. Unfortunately, it appears whoever...
The simplest way to check if they work is with your multimeter. You just want to make certain there is continuity between each pair of connections, and the impedance (whatever it is) should be the same for every speaker, if the speakers are all the same.
It would help going forward if you...