Get in the crawlspace and shore up the floor system. Do as you plan for the wall but don't "jack it up" "shore it up". If you don't want to remove the rotten joists at least coat them with a rot stopping product.

I don't think the shiplap was a layer of siding, I think it was the original sheathing and could very well have been left alone.
_________________________
Have you ever listened to someone for a while and wondered..."who ties your shoelaces for you?"