I grew up in an area where many houses were damaged by mine subsidence. See link.
Damaged Homes Photo Gallery
Some houses were unsalvageable. For those that could be repaired, basement jacks under the floor joists were used to raise the house and new foundation walls on 5 foot deep footers were built. Permanent lally columns were installed to give the floor extra support. Cost was usually $3,000 to $5,000 (about $15,000 to $25,000 in constant dollars).
The damage to your house does not seem that bad. Most every house settles eventually. Unless your house is built on unstable fill or ground or a swale and likely to settle further, I'd go with the jacks in your crawl space. The 20 push piers are overkill.