If I understand correctly the premise is as follows:
1. With the cutter on axis above the work a convex profile is produced, as illustrated by the OP
2. With the cutter off axis by more than its diameter (and presumably offset in Z too) then a concave profile is produced
3. Between the convex profile (1) and the concave profile (2) there is a point where the cutter produces a profile that is neither convex nor concave, ie, it produces a cylinder
I agree with 1 and 2, but I do not see how 3 follows as a consequence. I do not think that 3 follows from 1 and 2 because the effects in 1 and 2 are produced in different ways. The convex profile in 1 is produced as a result of the clearance angle on the bottom of the cutter. If the cutter was flat across the bottom, as requested by the OP, then it would not produce a convex profile. The concave profile in 2 is produced by the intersection of the circular cutter and the rotating work. It makes no difference if the bottom of the cutter is flat or concave.
There is a point at which the cutter will produce a profile that is neither convex nor concave, but it is when the cutter is offset such that it touches the work at a single point, and therefore isn't really cutting.
Regards,
Andrew