Just pointing out some things:
1. Bolton is keeper of The North because of and nothing but his loyalty to the Lannisters; are the Lannisters going to give up their hold over him by simply letting him get away with a scheme that they can stop in its track untill Bolton has paid a handsome price for it? Not to mention that the Lannisters would have to overlook an act of high treason that lead to the death of King Joffrey?
2. Bolton is the keeper of The North because of his betrayal of the King in The North; he wouldn't gain much by replacing a notorious claim to The North with a shared claim to The North (that as we know 'remembers')
3. Bolton'a best chance to hold on to The North is by turning on King Tommen and pledge allegiance to King Stannis (if Stannis would be stupid enough to trust a man who betrayed his liege twice already rather than put his head on a stake.
4. King Stannis would see it as an affront if Bolton solidifies his hold on The North by anything other than bending the knee to Stannis first
In short; I think Littlefinger is either overplaying his hand or playing yet another long game we can't oversee.