Not to minimize what has gone before, but IMO that process description is the most valuable info in this thread.
If I decide to attempt getting that "perfect" fit, My process would be what
@Dabbler has described.
To clarify, for people that don't have experience with lapping films, they are very tightly controlled precision abrasives. The "film" is usually a .003" flexible plastic backer sheet (or strip) with the Aluminum Oxide (A/O) or diamond abrasive grit "bonded" to one side. I say "bonded" but I have no idea how they actually attach such fine abrasive media. The various grits are graded in microns and run from at least 80 micron (course) down to fractional micron. I think I have some .3 micron, which is extremely fine and can achieve an almost mirror-like finish. As a point of reference, I find that 30 micron cuts about like 600 grit wet-or-dry silicon carbide on steel. I like to keep the abrasive action wet with light fluid (even WD-40) to help flush away the cuttings. Microabrasives will clog up fast on a dirty or dry workpiece. I was introduced to microabrasive films during my career and have accumulated a substantial collection over the years, at reasonable prices, from eBay. 3M is a primary manufacturer, but there are others. You can't go wrong with the 3M microabrasives.
Back to lapping the taper on the chuck: Microabrasives are available with Pressure Sensitive Adhesive (PSA) on the back of the film. I would use PSA film and cut it to a
truncated cone flat layout form and apply it to the spindle taper on my lathe. I would size the film flat layout so it protruded about .06" beyond the front face of the spindle taper, so that it can reach to the bottom of the female taper. By cutting the flat layout into maybe 6 or 8 segments (rather than one contiguous piece) and leaving a small gap between each segment, the gaps will allow the cuttings a place to escape. By applying the film to the spindle taper, the lapping will not introduce any angular or out-of-round error.
Safety Concern: I've described using the lathe spindle as the master for the lapping process. However, how are you going to achieve the motion needed to actually lap? Here's an idea for your consideration. Ahead of time, prepare a 1" or larger steel bar (as long as practicable) with a center drill recess in one end and attach (weld?), perpendicular, a piece of stock of adequate length to prevent the bar from rotating (anti-rotation arm) on your lathe. Tighten one end of the bar into the chuck, put the chuck onto the spindle/microabrasive and engage a tailstock center into the tail end of the bar. The tailstock can provide the necessary axial force and the anti-rotation arm's purpose is obvious. Pad the contact area between the anti-rotation arm and the lathe to prevent damage. It would also be good if you could apply a vertical force to effectively make the chuck weightless.
The described process allows both of your hands to be away from the chuck while the chuck is in a position to be lapped. One hand can keep the WD-40 flowing to the lapping zone, and control the tailstock pressure while the other hand could control the rotation of the spindle (wrench in camlock?). Proceed with caution and check the fit frequently.
The reason I titled that paragraph "Safety Concern" is the obvious (to me) temptation to use the lathe spindle under power to achieve the lapping action. The slowest RPM on many lathes is way too fast for the process, IMO.
If you can make a separate lapping mandrel, the whole process would be a lot simpler with the chuck on the bench, in a vertical orientation. That way, gravity becomes a non-issue and the lathe spindle is free for test fitting without having to remove the lapping film. The trick is to make a lapping mandrel with the precisely correct taper. I would have made that last sentence all caps and bold, but . . .
