Why not just let Four strangle Tris? I mean, it would prove that he's actually being controlled and not faking it, wouldn't it? If he was faking it and expected the guards to pull him off of her, then he can now run around and keep faking it without suspicion. But if he really was forced to strangle his girlfriend, wouldn't it prove that your new serum worked?
Especially since Tris is supposed to be executed in about sixty seconds anyway - it's not like she's being saved because she's useful for anything. There wouldn't even have been any blood to clean up, if that's what Rita Skeeter the Erudite woman was afraid of.