/diy/ - Do It Yourself

Didn't see anything like a welding general so guess I'm killing a thread.
Pic related is inside my car door, it's one of the window regulator mounts. It's stamped sheet metal spot welded to the inner half of the door, which is then welded to the outer half. As such the only access I have is through this 1"x2" hole.
I've already talked to several shops and none of them are willing to touch the repair. Most have told me I need a new door, which I completely understand but would like to avoid. It's kind of a shame to scrap the whole thing because of one shitty broken bit, and I'd have to get a paint match done.
I can afford to get the door replaced but I'd like to try fixing it myself first. Only problem is I have no experience welding, so I'd like some advice there. The plan would be to pick out an appropriate welder for this job, then buy a bunch of sheet metal and practice until I'm confident and then some.
My constraints are I only have access to 120V, and I'd like to keep the cost of the welder (minus consumables, gloves, etc.) to the 'several hundreds' vs. 'many hundreds.' I briefly looked at stick welders (due to the size of the hole) but now I'm looking at small-nozzle MIGs.