PLEASE, especially for surrounds , don't get into this "quality of the freeking wire" snake oil chain. For under carpet you want wire flat so you don't have a big hump, and tough so it wont break or wear through and short. Almost anything is sufficient for surrounds. A perfectly viable alternative for surrounds is RF or IR links. For surrounds, 18 Ga if fine. Who cares if a fraction of an Ohm difference would roll off the surround at 35 instead of 30 Hz? This is only physics. No magic needed.
The most trusted cable supplier is Blue Jeans Cable.
Most popular cheap cables are Monoprice and CableMart. If nothing else, read their white papers. No idea if they have flat cables or not.
Instead of slitting your carpet, a standard electrical wire snake will work for 20 feet at least. You don't want a slit down the middle of the room. You'd be better to go rent a kicker and pull the carpet back from one wall, run the cables and kick it back.