Cutting down an axle tube

I do think you will have problems with distortion after welding if you don't use the proper jig.

You are right, I do this for a living and have seen axles that are bananad from this kind of narrowing. I dont mean to knock the OPs project, however this is not the right way to do it. A proper fixture has 4 round machined pieces that slide onto a solid steel machined straight bar, the 2 round pieces bolt into the carrier and the other 2 slide onto the ends and square up the housing. Once all the inserts are tightened, then welding can begin. When you weld metal, no matter how thick it will distort when welded. Just ask any race car chassis builder. The jig helps minimize that. Dont feel bad since I have yet to see a straight housing yet, most are bent from curbs and such. Hell I bet Chrysler didn't even have them perfect.