8 3/4" narrowing - Dimension Help

Hey all, I have a relatively stock 74 dart swinger, and am looking to swap out the original 7 1/4” rear end (3507881) with a 8 3/4" rear (2881489). I’m planning to have a local machine shop narrow the 8 3/4” housing for me, but was trying to figure out what the final modified housing width should be. Here’s a rundown of the measurements:
The drum-to-drum difference is 3 3/8”. Does that mean the housing width of the 8 3/4" should be narrowed to 51 9/16” (54 15/16” minus 3 3/8”)?

I was planning to order new axles from Doctor Diff to put back in, but they are listing the stock A-body 8 3/4" housing width as 52 5/8”. That had me questioning my math. I was assuming I could order new axles for a stock A-body 8 3/4” housing, but the dimensions aren’t matching up. Perhaps that’s because the stock A-body 8 3/4" rears had the small bolt pattern and different drum brake dimensions?

Just want to make sure I don’t mess up a perfectly good housing (and waste my money)!!! If my math is correct and the housing should be narrowed to 51 9/16", I'm assuming I'll need to order a custom length axle package from Doctor Diff to stick back in.

Thanks!