What would cause a toilet tank to intermittently leak into the bowl only when half-full or more, even after a flush valve replacement?
All I can think of is you are developing a siphon between the tank and the bowl. How high does the water get to the top of the overflow? The overflow pipe is the one that sticks up in the tank.

I would try to set the float level (what ever kind of float it has) such that the water in the tank is an inch below the top of the overflow pipe and see what happens.