Monty, in the UK about £1000 allowing for a modicum of engraving, jointing etc. Turn round about 2-4 months.
Welder, can't think of many advantages either way other than the aesthetics.
Arguably there is a risk of cracking in TIG process if the barrels are not properly normalised after welding.
Also I have come across many soft solder sleeved guns that are loose in the joint. This should not be a safety issue but accelerates the appearance of the joint as a silver line. It is only really detectable at the breech face where under magnification one can see oil bubbles being blown when you flex the tubes, similar to the test for loose lumps.
As regards sourcing tubes, I think most come from Italy ready machined. No idea where the US ones come from