When we mounted a new diamond wheel on the grinder hub we dressed and trued it by grinding a piece of softer steel. the steel would break down the bonding agent releasing the diamonds and true the wheel up. A cleaning with the white stick and it would grind carbide to a mirror finish.
With a die grinder mounted in the tool post I have ground in lathe 3 jaw chucks but this was with 3/8" shank bits and a heavy die grinder.. THe came out very good and would normally run under ,001 until some one put a pipe on them.
With a 1/8" shank mounted point in a light die grinder dressed properly extended 1"+ ahead of the collet. The play in most die grinders bearings leverage of the extended point ad slow speed of the grinder ( a 1/4" mounted point should be running in the 50000 rpm range) grinding straight true and round is going to be hard. On the lathe straight is going to depend on the machine as there is no "adjustment" for taper from the carriage travel alone. With this set up .002-.005 run out ,roundness and straight ( TIR ) would be good.
With a solid heald, parker majestic, moore or other ID grinder things will be much better. In this machine With this set up holding .001 should be no problem you have the means of adjusting for taper. a spindle thats running up to speed can dress the wheel much better and truer.You also have better control of size and depth. These machines are not always available in most machine shops let alone a hobby shop.
What might be quicker easier and more accurate for what you want to do is a small carbide boring bar in the tool post sharpened and honed to a fine edge. A 5/16" bar with extended 1" or so will be much stiffer than the 1/8" shank wheel extended. It will be easier to cut true and round. set up will be easier. less spring in the tool also. Set up a boring head in the tailstovk and you have taper adjustment thru the tail stock.
Set up is going to be critical here the barrel will need to be running dead true to center. the boring bar sharp and set to center feeds and cuts will be light. Getting thetouvh to start that far in is going to be hard measuring the size that far in harder. Here pin gauges will be a plus. When setting up the bore of the barrel will need to be indicated in with a sug pin then the chamber checked if your lucky they will both be centered if not then one will need to be "fudged in".
I would think the starting point would be a good chamber cast to see what is there for sure and certain. This will show what your working with. for the touch off of the tool a this brass ring fitted to the chamber end and a .030 wall thickness allows a touch where it can be seen and at a known point. Here once touch is made come out .025 and feed in .001 a pass until desired size is reached.