I've looked carefully through this thread and couldn't find any information as to what make of action you have. This matters since different actions are made from different steels. Also access to the rails is more or less difficult depending on the make of the action.
In general, you can weld quite a bit on the rear of a receiver and not have to concern yourself with heat treating.
Silver solder is not always the best approach since the temperature required is hot enough to significantly alter the hardness of some steels.
A TIG welder uses a tungsten rod as an electrode to melt the parent metal and a filler rod for build-up. A good TIG operator can weld about anything and get good results. If I wanted to have something like this welded, I would strip it down and take it down to SAIT. There are always guys there who are re-certifying or something and would be able to do it for you. If I had all the particulars (action type etc.) I could furnish instructions if desired.
It used to be common practice (well, mabe not common) to cut two mauser actions in half at different points then weld the two long halves together to make a long action and the two short halves to make a short action. Many of us did this just as a project.
Anyway, if you are able to smooth it off and the cartridges are still retained in the magazine OK, you are probably on the right track. GD