Hi there. I am a structural engineer who lives and practices in Florida. I am familiar with situations like yours.
Before you do any repair work, please hire a competent structural engineer to evaluate the settlement and its causes. This is a serious issue in my opinion; to simply rely on contractors to solve your problem may not be your best choice. The engineer may retain a geotechnical engineer to take boring samples of the soil layer beneath your slab/house. Ground penetrating radar may be useful in finding out if any voids exist under the slab.
Once the source or reason for settling is discovered, corrective action can be developed by your engineer. There are many techniques available to stop the settlement and to control/prevent future settlement. Some of these techniques are:
1. Use of needle type piles
2. Under pinning using helical type anchors
3. Injecting cement/rout under the slab
4. Injecting urethane type material that will expand, fill voids and expel any present water from the voids under the slab (one commercially available material that I used in the past to correct apron to Navy hangar is URETEK; this is a link to their web site
As far as the expense, it all depends on the corrective measure to be implemented and the size of the project and types of equipment to be used. Once a plan of action is drawn, I recommend that you compete the construction portion between three to four qualified and experienced contractors.