If the underlying cause is sinking/moving soil, I think you have a big problem.
(On a tangent,) here, in SE PA, the city of Philadelphia just condemned about 30 homes due to walls separating, foundations sinking, etc., etc., because they were built 60 years ago (before codes were in vogue) on top of an ash fill. Coal ash! An underground stream got a 'kick in the pants' when the city dug up the street in front of the homes to repair a leaking water pipe. The underground stream water filled the dug-out hole and began eroding away at the ash. In time, the displaced ash was not replaced with anything but air! Hence, a large number of interspersed cavities underground were created, and the homes began to sink! The city has avoided a law suit and paid to condem the homes and help relocate the residents.
Unfortunately, it may be too late to correct what has happened under your slab. You could consult a structural engineer before you do any digging. If your neighbor(s) is/are doing the damage, you may be able to sue. But if it's a direct cause of you pumping well water, you may be in a tough position. I'd have an engineer take a look before the township authorities make an appearance. Geesh, I wish I could give you my better $.02 worth. I hope the engineer proves me wrong! My best to ya and hope this helps.