I know the methods that worked best for me involved concrete pylons being poured under the home that were really deep.
This.

My parents had trouble with one corner of their house settling, so they had it mud-jacked (It was built in 1960). Ten years later the problem was back. Mom had a contractor come out and put pylons down to the bedrock which were then bolted to the foundation. In the corner where the problem was, it was about 30 feet to bedrock. Just a few feet in either direction it was only about 12 feet. Apparently there was an underground spring at that corner.

I think there ended up being 5-7 pylons poured. It cost mom around $45,000.