This is my 2nd reply; other did not post. As others said fix the
problem first. Visit your local home builders assn. They'll advise
you. You may even find a Gc or sub there between jobs. I'd suggest
even extending the foundation. You could use the extra basement space.
Be sure to have him "mother" all floor joists the full length once
they are relevelled. That means adding studs on each side of each
joist to increase their structural capacity.