OK, I've been sitting back and reading this whole time.
I'll go ahead and add my $.02
The carriers I've welded in the past I've either stick welded or TIG. However, TIG gets to be too cumbersome and I usually resort to a 7018 on the stick welder in the end. Most have been stick welded with a 7018 and I've yet to have one come back because of a failed weld.
Personally, I haven't MIG welded a diff, but I've seen it done by several people. I don't see why it wouldn't work if its cranked up all the way for good penetration.
Do pre-heat cause it burns off the oil and impurities (important when MIG welding, but doesn't matter as much with stick), it well, pre-heats the metal and gives a better flow for the metal (gets the molecules ready to be welded!!!), and the gears are heat-treated and its always good to pre-heat heat treated metals because of their odd welding characteristics.
All the ones I've welded, I welded the gears first, then welded the gears to the carrier (except the $$$$ 14 bolt carrier). If you run moderate sized tires, weld just the gears, and you should be fine. If you run high HP and big ass tires, weld gears and gears to carrier. IMO.
I've done both and both have held up. I think it all has to do with the welder (person, not machine) doing the work. Quality welds equal better performance with less welding than booger welds all over the whole thing equals same performance with much more work/welding. Put some good quality, high heat welds in there on just the gears and you should be fine. If you don't think your skills aren't up to the "quality welds" standards, then put more weld on there and weld the gears to the carrier.
I wouldn't worry about it being cast, you're putting so much weld in there it will not matter. I've never had the "cast" as being an issue when welding the diff.