Ooh, I like this. Might steal for my own plan or switch my vote.
Mind you, this plan is risky in that it relies on a very specific sequence of events occurring. If Varys' spies can get word to the Riverlands faster than Tywin can get his army there, we're golden - Gregor's men are little better than bandits and thieves, and they're Lannister men. They might fear him, but if they hear we've turned on Gregor, they'll assume Tywin has as well (after all, it's not like they have good communications), and they fear Tywin more. Gregor's as vulnerable as anyone else when he's asleep.
If Tywin manages to move faster than OTL, though, the plan fails. The moment Gregor rejoins the main Westerlands host and his men realise that Tywin didn't betray Gregor, they won't dare make a move no matter how much coin we offer. In that case, the Riverlands and Westerlands end up at war, likely dragging in the Starks, and we look like ineffectual idiots.
I think the plan has a good chance of success - individual spies move way faster than an army, and I'm guessing Varys has some sort of relay system to get news across the Kingdoms quickly. Meanwhile, Tywin's not in a huge hurry - he doesn't care if Tyrion dies, so he'll be happy to wait a little longer to gather as many troops as possible before invading.
As for why Tywin would go along with pretending to be enforcing the King's Peace? Sexism. If Tywin publically admits that we had one of his bannermen killed, then he's admitting that his daughter - a woman - outmaneuvered him, and that he can't control his own family. He'd be laughed at openly, and his ego would never allow that. We're offering him an out, by letting him pretend the whole thing was his idea.