Have a Savage Stealth in 338 Lapua, looking at going to Lapua Improved (don't ask why). I don't see any issues with the rifle but the magazine looks like it could be problematic.

1-Not sure if it's wide enough at the shoulder, and

2-There are guide ribs pressed into the mag which hold the round (so presumably it doesn't bang against the front of the mag). I don't think the Imrpoved version would fit (see picture with round pushed back as far as it would go).

Has anyone done this conversion with this type of Savage magazine?

Just converted two 110s to 338 Norma. One Elite Precision and one LRH. I know, not what you asked.
I am sure you can solve the mag issue.

Can't help with the answer but would love to know the Why?

Me too, but he said don't ask why. It makes absolutely zero sense, but we will never know.