Hi, and welcome to the forum!
Don't worry about the existing wires being larger. That shouldn't present a problem at all.
You also can use the pre-wiring in conjunction with those speaker connections. If you have friends that are good with this stuff, it might be best to have them help. It's not too difficult, though. The speakers have cables with two wires coming out of them. Those two wires are then terminated in those connectors that plug into the main unit. The easiest way to do it would be to cut the wires, leaving you with two bare wires coming out of the speaker, and two bare wires with a connector on the other end. You'd plug the connector into the main unit and connect the two bare wires to the pre-wired cables on the TV side, then connect the speaker ends to the pre-wired cables on the back wall.
You could certainly get a different system, but if you're happy with what you have, you can definitely make it work with the pre-wiring.