I dunno, anyone who wants to MIG on a barrel lug as opposed to TIG ain't much of a welder, so right off I suspect their gunsmithing. Why go through all trouble? A stock G34 is very accurate, I find better than the 17 just due to sight radius. Want more? Fix the trigger up, put some real sights on it or fit a Bar-Sto barrel into it.
How accurate do you need? I can keep 90% of my shots in the black at 25 yds on a NRA B-6 25yd bull. That is better than minute of steel plate accuracy.
Now for my 17/34 opinion. Get both, just get the 17 first. I have 2 17s and I prefer them because they are Gen IIs with no stupid finger grooves and big frame rails. The 17 for me points better and controls in recoil better, it will move for me striaght up, straight down. With the 34 ( I have one) I get kinda a little figure 8 track to the front sight when shooting fast. What I'm saying is a little muzzle heavy and I don't like the grip. The 17 you can conceal a little better, and that is about it. FWIW, I killed a frame rail off on my 34 after 35K rounds, it was one of the ones subject to the recall.
Whichever one you get, change the sights, grip tape it up, clean up the trigger and shoot it til it smokes.