Did you drain the fuel strainer, or did you just sump the tank? I have seen major corrosion in strainer bowls, indicative of strainers that seldom get drained. If it fills with water it can't prevent that water from getting to the engine, and if it was already full it needed only a few drops more to make trouble.
The newer 172s have the boost pump under the floorboards under the copilot's feet, right at the lowest point.
Vapor lock in high-wing airplanes is rare indeed. The head pressure of gravity is enough to prevent it.
Those newer 172s also have 13 sump drains. Five in each tank, to get all the water that comes up against internal stiffeners, one under the selector valve on the belly, one under the header tank (also on the belly) and the fuel strainer. Got to get them all. The header is there to get the return fuel that has bubbles in it.
And a sticking valve is a definite possibility. Is this a rental that get flown full rich much of the time?
One further possibility: There were a number of fuel distributors (the thing that divides the fuel four ways, to each cylinder, and sits atop the engine) that were manufactured with too-tight clearances. The shutoff poppet can stick, and usually shows up as a hard-starting engine in cold weather. Should be an SB on it on Precision Airmotive's website.
Dan