If you weld you WILL anneal the area you have welded. The only question is how much of the area. Tig would be the ideal process, and ideally again, pull the barrell and screw in a large brass plug to act as a heat sink. Wrap the back of the action in wet towels.
The easier idea is to make up a dummy dove tail piece slightly over size, tap it in, then file it to match the original contour and touch up with cold blue or parkerize.
Strength wise i wouldn't worry about that cut at all, but wow, don't you wish you could slap the bubba who did that?