I've been brain storming a solution for you. It might be a bit more involved than you would like... but it should work:
Since you're dictating the chamfer dimension for both from a parameter, why not use that information for your rigid join along the lower center point?
For instance, if you know the diameter of the thumb screw to be 1/4" and the chamfer to be a 1/4" on the thumb screw and a 1/4" on the recess, then your parameter for the rigid on center will be 0.
If you increase the chamfer on the thumb screw to 1/2" the offset remains the same: 0
If you increase the chamfer on the recess to 1/2" (thumb screw is 1/4") the offset is: 0
(unless of course you are determining height from another point; threads, standoffs, etc)
The only time I can think of in which the offset would not be 0 is if the chamfer on the recess is steeper than the chamfer on the thumb screw, or if the ID of the chamfer is greater than the OD of the thumb screw. In the latter case it's a relatively simple math problem to ping the parameters for the diameters and chamfers to dictate the offset:
(For an symetrical chamfer) Offset is equal to (ID-OD)/2.
For an asymetrical chamfer it gets a little more involved so I won't go in to it unless you need me to.
Does that help at all?