Question on lapping 378674 mould for PPing in .375 H & H

After trying this boolit paper patched after sizing the driving bands to slightly over bore diameter, I'd like to see if I could improve accuracy by lapping a portion of the nose larger, as it is well under bore diameter and practically rattled when I placed it in the muzzle of the rifle to check nose fit. Actually, it tapers from .365" to .352" over the first .300" directly ahead of the initial driving band. The ogive begins at this .300" point and forms a semi-spitzer shaped boolit. My question refers to pdawg shooters suggestion that the bore riding portion of the boolit be lapped to the same diameter as the driving bands. Do I need to try to form a cylinder shaped section of the same diameter ( .367" to fit bore) over the full .300" length, or is some taper in this section acceptable?

Lapping is good to increase size and maintain the original shape or contours. It gets trickier changing when changing the shape or form as lapps need to be turned or formed in the new shape. A brass lapp turned up to what you want may do the job but would need to be supported in some way also.

What might be an easier solution would be to acquire A lee mould in a smaller caliber. Buy a drill in the dia you want and Grind a form drill with the nose shape you desire. This can be done by hand in a pedestal grinder to get the basic shape. then back of the cutting edge by hand with a stone. Align blocks in drill press with the drill ( use a vice to hold them) and drill to depth with the form drill and lots of oil. Then lap to final size. This will give you what your wanting