Frame
A ton of progress! I decided to attach the stainless skin to the wall framing with 3M CV62F VHB tape which took some time to source since it's more of a commercial grade product. The walls are pretty flat but not perfect due to normal weld distortion so the 1.5mm-ish thick VHB will hopefully allow the skin to not mirror every minor imperfection in the wall framing. Also trying to weld extremely thin 20ga stainless to 14ga carbon steel (and 1/8" carbon steel in some spots) is much more difficult. I will still be welding the seams on the stainless but will avoid tape near the welded seams.
Tests with the laser setup show it is not tolerant of large gaps at all so fit-up of the skin panels will be key. If the skin panel fit-up is too hard to get within tolerance of the laser welding, I will simply add some cap and trim pieces and then weld those on which would be MUCH easier despite more welding. The laser welding takes a fraction of the time of regular welding though and not having to fuss with fitting the panels makes me tempted to just use trim pieces in the first place.
For the paint I went with an industrial epoxy: Rustoleum 9100 Mastic. It's a super durable 2-part epoxy and should help seal the welds on the floor panels. I decided to roll it on due to concerns of overspray in the rental garage and the owner not wanting orange paint overspray on the walls which we were originally going to spray it and cover the walls with plastic sheeting, but rolling was much less messy.