Good job Billy Joe. You can help us more often. I may add that I don't trust hydraulic jacks to hold very long. Use a heavy hydraulic jack for the initial jacking (with a metal plate above the jack)and then use screw jacks, blocks, or beams and shims to block the house up. Watch out for railroad ties and beams splitting or breaking in the middle. If very muddy, you may want to recheck for settling for a day or two while you are rebuilding your piers. When jacking heavy weight, stay to the side cause they can kick back at you if they slip.
You can get by with one heavy jack or two if you use other bracing materials. If doing the whole side of a house, you may not move one corner as much as you want the first time. When it jacks as much as it can, then block it and move down the rest of the side and then come back. You will probably end up leveling the whole house. As Billy Joe indicated, basement concrete floors aren't poured supports everywhere and don't usually have footings except in load bearing places so a jack in the middle of the floor will break it out so use a railroad tie or beam on the floor to spread the weight.
By the way, what do you guys use for hurricane ties to tie the houses to these piers? And around here we have hard ground with frost, maybe Billy Joe can enlighten me as to how deep and what type of pier base support is used (rock, sand, etc) assuming they don't drive piles under houses? Thanks.