Narrowing a 8 3/4 diff.

I know it doesn't help you, now. And I realize you're doing this in your garage, in the great white North and all. But, the machinist in me, tells me I would have done this (part 1, anyway) differently. I would have chucked up one end of the hsg in a lathe in a four jaw chuck, with a live center/cone in the other end. Then I would have cut rings in the OD of the tube for running a steady rest. Then I'd place the same end in a steady rest, and removed the tailstock. Then I would cut the tailstock tube end off with a parting tool. I think I'd try (if the tube is thick enough)to cut a precision register on the tube end. This will mate with a female register I'd cut in the shortened brg end just removed. The other side would be pretty much a repeat.
@rustycowll69 i appreciate the feedback. I only have access to a lathe for small periods and projects when workload permits. I'm not a machinist by trade. I wish I could do a lot more there. I'm actually a non destructive testing technician. So I usually critique others welds for a living.
This time I will try to get my final welds x ray'd and show them in the final video. I don't think the factory tolerances were do tight either.
From these pics do you think the housing was friction welded together?

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