I am loath to enter a discussion on welding in case I attract the ire of anybody but in case this can be of help:
I know that the main barrel specialist who specialises in TIG sleeving always heats the tubes around the welded joint to normalisation temperature after the joint is welded. He can then strike off the weld and strike up the barrels. We welds using mild steel wire/rods.
He has said to me that he needs to heat up the tubes to 'allow the carbon the migrate and even up its distribution'.
I have never had any problems with hardness after this process but I will say that the zone along the weld joint (about 5-7mm wide) always polishes to a brighter finish than either side of it and doesn't black quite as darkly.
However, with the guns in my own modest collection, I have found that the darkness of the blacking evens out over 12 months or so and becomes pretty much invisible even after re-blacking.
The above are observations only. I leave the technical comments to any professionals watching.