Expanded good info from Daryl, thanks for that.
Just looked up the .375 2 1/2 and .405
The .375 is .059" total so .0295 taper per side
The .405 is .0244 total, so .0122 taper per side

Interestingly enough, if I degrease cartridge and chamber with Acetone my .375 2 1/2" Flanged Mannlicher will in fact grip the chamber on firing as one can measure/feel a small protrusion of the primer commensurate with about .002"-.003" headspace. If it did not grip, the primer would be pushed back in flush with the case head.
- Mike