I have personally Jacked Up homes, made an entryway into the basement with a Backhoe (ramp), used a BobCat to remove the wall(s), set concrete forms, and poured a new wall(s).
I only jacked the house up enough to let the pressure off the basement walls, very little, not even enough to crack any sheetrock inside.
The cost was not that bad actually, it took me and my partner about two weeks to complete the job, if I remember correctly the wall was about 30 ft. long. We did this to several homes, the money was good and I enjoyed doing that type of work 25 years ago--:

))
We dug a channel below the footing for a 4 in. perforated black plastic pipe and directed it to a sump hole we made under the footing into the basement floor, filled everything with Pea Stone, covered the Pea Stone so dirt would not stop water, made the footing pour with a lot of rebar, set our concrete forms, made our pour, set the house back down, tied it to the new foundation, backfilled, dressed the yard up for seed and were out of there, they have never had a problem since to my knowledge.