So, after doing some reading, is it better to let the yeast finish what they're doing and back sweeten instead of trying to stop the fermentation?
Correct. Unless you have the ability to cold crash and filter it's very difficult to stop an active fermentation.
But if back sweetened, you still have to add stabilizers to keep fermentation from starting back up? Seems like a potayto-potahto situation.
Yes. If you don't stabilize it, the remaining yeast wake up and keep fermenting. You let the mead clear so that the yeast fall out of suspension. You want as little yeast left as possible before stabilizing.