Bob-

First thing I want to note is that you're presenting yourself and this rifle as a very good example for the men out there who are on the fence as to whether or not to take such a project on -- you've done a really good looking job on your rifle and this will certainly affect the way some guys will view the possibility of building their own doublerifle form a shotgun action.

Next, on tig welding...
I'm a highly qualified welder, tig is one of many processes that I command with relative ease.
You need to ditch your welding shop and find a new welder.

Your profile doesn't tell me where you live, if you can tell me what area, or better yet what city you live in I can do a little searching for you and point you in the direction of where to look for a welding/engineering shop suitable for the kind of work you're doing.
It's clear to me that the guys you've been going to are WAY below your standard and to an extent pose a risk to you and your work.

That just is.

Furthermore, I have a good sense you would likely be a good candidate for training on a fast-track schedule, and if you were to take the interest you could become a very good welder - tig or otherwise- in a relatively short time if you wanted to go there.
You could get into a tig machine much better than good enough for the work you need done in the $800-1800 range.
Consider it.

Seriously consider ditching the welding shop you've been patronizing.

--Tinker