Michael Bateman produced a large number of helpful articles about building 160/175 racing machines which I loaded into Group W's FB site years ago under "Files", it's all still there for review and here's a sample:
"A 175 tranny can be fit in a 160 case without too much work, but you do need a milling machine to do it as you need to modify the cases to fit the shift drum – both style 175s have a ball bearing on the shift drum. It’s easiest to have both cases and both transmissions sitting side by side so you can see what needs to be done. A vert 175 tranny fits directly in the sloper case. The vert shift drum and detent mechanism can be fit in the sloper case as well. It does take a little milling machine work, but it’s not particularly difficult. It’s completely worthwhile to use the later detent mechanism if you have the time and capability to fit it. The sloper 175 has a detent mechanism the same as a 160 but with one more cutout in the plate."
I don't recall any welding being necessary.