The folk at the NSSA would be who I would contact. They know 2-3 folk making custom barrels, (much like the originals), that do well.
Your other best bet is to find a 70's-80's made Parker Hale Enfield, (English made) due to their having a progressive depth barrel. I do not know if the new ones have that. A friend of mine has a "new" PH, and on the outside, it's a repro Euroarms.
Even the old PH's have a 2 piece stock, joined under the lower band. The Lock Plate & parts are still cast, just like ArmiSport, and Euroarms.
Lodgewood Manufacturing can set you up with a "de-farbed" Repro, but you still will only get a repro, with corect markings. The quality of the barrel & stock will still be what the Italians send over. You would have a lot of stock work to do to mirror an original. We won't even discuss what your point of aim/point of impact will be, that too, may require a lot of work.
The Company Quartermaster offers a de-farbed 3-band ArmiSport Enfield, but you may not like the ground-out Lock Plate marking, replaced with a more correct one. You will still have a less than quality repro, with the same incorrect stock shape.
Untill a few years ago, you could get an original for a lot less than what you have to pay for one now. A friend has an original 1861 Springfield that is a great shooter.
I have no technical data, I just know how much work it is to try to correct the shortcomings of what the Italians are producing. Try converting a Euroarms 3-band into a Second Model Enfield, like I did...I don't want to do it again!