What is the largest contour a guy could put on a Mark V magnum action without getting too whippy for the action.

Thinking the 378 is going to get a new 338/378 Barrel very heavy and very long.

I have what is called HV (Heavy Varmint) in benchrest. Barrel was 26" and from memory the muzzle diameter is about an inch. It was a 338/378 and the action came from a 416 Wby I had.

The HV taper could be regarded as being the first step down from a straight bull barrel.

There is no limit because you are going to bed the first 2 or 3 inches of it anyway. So, Receiver diameter, full length, is probably over kill.
I install 1.25 no taper, bulls all the time on all sorts of receivers.