Sounds like a lot more work than necessary... can the breech/plug be tweaked so you can rotate the stamping to the bottom?
What are we talking, round or octagon (what maker)?
You could also cut the area out and inset a small brass/whatever plate for your own marking.
As far as welding... sure, I suppose - I would not be too worried about warping in the last 3/4 inches of a barrel at the breech end being a problem.
Again, welding and machining sounds like a lot of work - sure it will work, but I would be looking for other solutions....
Honestly, I would grab some anti-oxidation coating, smear it inside the barrel (alternatives are Inert Gas fill, like, using your shielding gas, or just take your chances), and try to keep the heat inputs down as well as possible.
Everything from old Cooeys, to TC Contenders, uses a welded on block as the basis for the joining of the barrel and action.
Despite the hand-wringers suppositions, barrels are not that special, as far as alloys go. They tend to lean heavily towards 'easy to machine', or 'easy to displace' (button rifling), and other than a few outfits selling their secret snake oil treatments, whether they are heat or cold based (both, forms of heat treatment).
Feinwerkbau, a German maker of Olympic quality firearms and air arms, built a pistol, that had the barrel do a complete loop around the compressed gas cylinder. It shot as well as their other fine products!
https://images.proxibid.com/AuctionImages/3693/253387/FullSize/236-7.jpg
This was largely accepted as proof that what happens in the last bit of the barrel, means a LOT more than what happens in the rest of it.