Have been having a think about this.
(1) The advantage of 'doing it yourself' is that you can spread the cost of work on your rifle at your pace, as and when you have the money to fund it. However - bear in mind that you will almost certainly end up paying more than if you can lay out the cash in one instalment.
(2) In the forthcoming Holts auction, there are at least three Westley Richards (all proofed for black powder), and one Jeffery (in .303), single-shot/ Martini actioned rifles (all around lot 700). There is also - ta da! -
this rifle, which may be of interest. I have never heard of the maker or cartridge. I suspect that I can guess where the action came from and, with a bit of luck, you might be able to pick up a completed rifle in the UK for the price of an action in the US.
From France, a WR Martini action in - ? - .450:
https://www.interencheres.com/meubles-objets-art/militaria-296514/lot-29871920.html NB - buying from France is a bit bureaucratic nowadays, but not insurmountably so. Still a pain the arse, though.
(3) The falling-block action is an extremely strong action. The actions that are proofed for black powder
ought to be strong enough to support a nitro cartridge (not so the barrel, though). I am not an expert and - if you decide to use one of these rifle actions as a basis for a new build - you must take proper advice: I know where to go in the UK for such advice; not in the US, though.
(4) Finally, Nick Holt charges an outrageous 33% commission, and you will have shipping expenses, plus any import charges.