That "cut and weld" you speak of seems pretty intensive. Not sure I would go that way, but I am not as skilled as you seem to be.
I have seen some guys use compressed air (just an air compressor and blow gun) to take out some smaller ones. But then I have also seen some guys balloon the tank doing that too. If trying, use lower psi first to make sure you don't blow it up. Another concern with doing it this way is that if you have any weak spots, like rusted welds, it may blow out that seal and now leak.
I had a Honda Accord that a paintless dent removal company removed some dents in and that worked incredibly well, in my opinion, but that metal was a bit thinner than a m/c tank.
If already thinking of welding, couldn't you just use a spot weld on slide hammer and then grind the welds down, sand, and finish?
Also, check out "lock out kits". They have a blow up air bag in the kit that you wedge in door and pump up to hold door slightly open so you can get the rod through and hit the unlock button.
but there may be cheaper ones.
Any way you can get in there with a adjustable crowbar with tape on end (to soften hard edge) and massage from inside?
Crowbars | Rentallaser. Uitlijnapparatuur voor het uitlijnen van uw machine
Mine is a Craftsman. Not too expensive and actually is pretty handy.
All I got for now.