Out of interest, why might MIG be better? By shrinkage, do you mean it's warping a bit as you go?
There's a knack to knowing what to weld up first, something that I never really mastered, but stainless does like to warp (obviously it likes to expand esp. compared to steel) esp. low gauges. Try and keep your amps low, to keep the heat input low, make sure you've tacked it all up first, try and keep your runs short, take your time etc. etc. You should be able to control the heat better with TIG.
Have you got the flanges bolted down? It might
help, but be warned that sometimes you can't get it off the jig after welding it all up, apparently