My first impression is the concrete is "monolithic" and floating on material that is not able to support it.
Without visiting the site is hard to diagnose. I feel it is a foundation problem, and that should be investigated first.
I'd check with Soil Conservation Service to determine if there is landslide activity on your site, or even adjacent.
Then, water intrusion under the slab should be investigated.
The "R" value of the native material should have been determined by the designer.
I'd hesitate spending any more $ on repairs until the above is determined.
Sometimes it is impossible to "stabilize" for a concrete surface and a "flexible" road bed would be appropriate.
Flex road-bed can be done in several ways and method determined after the first three above are determined.
My guess is if the entire drive is moving you have a deep seated sliding mass. If it's located in one or two areas it's water.
Loading and unloading the slab by driving on it pumps water in and out of the "structural section" and the "fines" in the gravel are pumped out thus destabalizing the road
Additionally forces of vehicles on the concrete can have the slab walking across the concrete/gravel contact plane, or more likely an undelaying slip plane of different soil types or native and fill constructed upon it..
Partial removal of the worse segments and de-watering (drain blanket with drain pipes) and install of a "geo-grid" may help.
Again too far away to tell, so get the soil engineer on site.