Building, shooting and hunting with these rifles has been a 50+ year interest of mine and I probably built some 25 - 30 with .17 and .20 cals. almost exclusively since 2000. 
Action choices favoring Win. hi wall, Stevs. 44 1/2 and Rem.-Hep.,w/2 or 3 Cadet Martinis thrown in. 
The rifle pictured here is a 1983 build on a Win. hi wall, D.S. triggered, coil spring action. Bbl. is chambered for the German 5.6 x 50 R mag. (A ballistic twin of the American .222 Rem. mag.) The bbl. is a Shilen 1:14” twist machined full octagon w/an integral 1/4 rib by my old friend + metal mentor, Emil Facuna.
I stocked this rifle from scratch w/exc. quality European walnut and the stock pattern has worked out well in the field. 
After testing it I settled on the 40 grn. Hornady ballistic tip at 3500 fps. and it will stay in 1/2” to 5/8” at 100 yards on any day I am “on”. The optics were upgraded in 2000 w/a Zeiss Diavari V 5-15 x 42 scope. A good move! 
In the 1980’s and 90’s this rifle often accompanied me to the S.Dakota prairie dog towns and it also accounted for several coyotes here in Illinois.
“Knowing all there is to know about single shot varmint rifles almost ranks up there with knowing all there is to know about braiding buggy whips.”
From John T. Amber circa 1983.

I think we tend to forget that single shot rifles lost some interest as the WWII boys returned home. I appreciate that many actions were saved by being made into varmint rifles. I too lament the lost many barrels made by the old craftsmen being lost. Here is a Winchester Highwall in .225 Win.

Love the comment: Knowing everything there is to know about Varmint rifles ranks right up there knowing how to braid buggy whips from John Amber, circa 1983. 
Actually, we used to have a neighbor who showed me how to make braided horse bridles and reins. They were beautiful! Still have one of his hanging on the wall.
If I ever get tired of these old single shots, maybe I can revitalize that old art!👍😆. Less I digress.

Well done varmint rifles have always held interest for me ever since reading "Wood Chucks, and Wood Chuck rifles" by Landis. My favorite single shot, is a Pfeifer built, stocked by Monty Kennedy, in a beautiful stick of Oregon Myrtle, and chambered in 220 SK or Saunders Krag. Always liked the cartridge and name!!   Krag

Valley, Ben Shelor is a name I haven't heard in many moons. Had lots of great conversations with him. Sure do miss him. moodyholler

I have a varmint project that's been on my mind for a good few years.

It would not involve wrecking an original vintage rifle.  I plan to use a BRC Borchardt action I currently have.  I will need a barrel and stock set.  I have the wood blank.

Can anybody suggest a meticulous gunsmith who would take on such a project and finish it in a reasonable time?

Background: This harkens back to the 1980s when I was quite active as a groundhog hunter.  I then had a Sharps Borchardt custom varmint rifle chambered in .225 Win.  It shot lights out and put an end to the careers of quite a few whistlepigs.  Here's the only photo from back in the day:

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Oh, I regret letting that rifle go.

Curly

I'll do it but loads have to be jacketed smokeless loads they were built for. 

Reduced loads, lead bullets and extreme overbore is asking for trouble.

More than that. It takes incentive.  What are we shooting for?