My experience with welding cast iron is limited and unsuccessful.
One more data point… the first shop that re-gear my front from 4.11 to 5.29 was Slee and those gears lasted 5 years of hard wheeling before the first ring and pinion failure. I do not believe Slee stripped the threads or the problem would have happened much sooner. The second re-gear only lasted 4 wheeling trips.
So you haven't done the re-gear job yourself... Just so you are aware, it's very tempting to drop the bearings and the adjuster nut into the open bearing seat, then drop the top cap on to capture the bearing and the nut at the same time. Then tighten the top cap down to capture the bearings and the nuts. Doing this has a HIGH probability of cross threading the cap and adjuster nut. Not saying that's what happened, but I can see it happening that way, because its so easy and temping to do. The nut is the softer part and should be the destroyed part, would buying a new nut get you rolling, or is it truly the cast iron threads that are boogered?
Brazing in the nut won't get you the desired results, braze doesn't "tack" like a welder. It flows like solder. The heat to get braze to flowing is high enough that it would anneal your carrier bearings.
You might be able to tack it in with a welder, but the cast iron side of the tack is going to be brittle as glass, if it doesn't crack out when cools.
All the proper repairs I can think of would require pulling the axel tubes off and either filling the buggered threads with braze, picking up the thread and re-cutting the repaired area or boring out the buggered threads, brazing in a sleeve and cutting new threads in virgin material. Then you'd have to get the axel tubes radially aligned and rewelded into the housing. My guess is, it would be cheaper to get a new axel housing rather than pay for the labor to fix it right, but I could be wrong. Might want to talk to a machine shop/race shop, they should have the equipment, but maybe not the experience or imagination to see the solution.