The video by Larry Potterfiedl referenced above, illustrates the method that I use and the straight type of reamers I use(commonly known in the trade as chucking reamers). Whilst good results can be had using the method, I would not attempt to ream 0.015" from a barrel in one reaming as illustrated by Potterfield in reaming the choke of the second barrel. My experience has been that one should ream 2 or 3 thousands of an inch at a time, up to the final 0.015". This, of course calls for a set of reamers numbering 10 or more per bore size of the gun (20 bore, 16 bore, 12 bore and so forth. However, one usually needs to finish the choke reaming with either lapping or honing.
Chucking reamers do not come from the manufacturer with a treaded hole in the back end of the reamer, but are soft enough on that end to allow drilling and tapping the hole using a lathe. Another point is that I have my pilot bushings placed on the reamer shaft with a collar on the reamer T handle shaft where the pilot bushing will not move up from the reamer shaft onto the T handle shaft during the reaming. Never turn the T handle counter clockwise after starting the reaming of a choke. It is a good idea to make up a set of reaming pilot bushings. I keep a 3/4 inch round bar of copper to make up a bushing quickly when I encounter a need for a size that I do not have.
I do not do a great deal of choke reaming, however if I did I would have a reamer manufacturer to make me a set of reamers with a two inch taper section at the front of the reamer with a two inch straight section following the taper.
One should also consider that reaming a choke from full choke to say 1/4 choke or cylinder bore will leave quite a long straight section of choke at the end of the barrel bore. Sometimes as long as 1 1/2 inches. Whilst this is not always an issue, it may become necessary to use a tapered reamer to shorten the long straight section in order to have the desired spread and pattern of shot.
For those of you interested in the art of patterning guns view the " A Look Inside Holland & Holland" video and watch Holland's master- Steve, work his magic with changing the patters and point of impact using ancient lapping methods and crude machinery. I need to ask Holland and Purdey's how many of their new guns are ordered with choke tubes. I suspect that in my life time that the majority of bespoke guns will be ordered with choke tubes and the art that Steve practices will fade into the past.