I don't know the situation between the City of Slaton and the Lubbock City/County... They've always been the odd one out.
Next. There have been continuous coverage issues with this system. A lot of these problems were billed as 'growing pains' from the beginning - think basements or large structures like dormitories - and factor in the sheer size of the county versus the terrain features like the canyons. I don't operate in those two specific areas, so I can't speak if there are any improvements in those areas.
As far as the Permian system, I believe it's a distance / Council of Government issue. Lubbock is in the South Plains Association of Governments, and the Permian is, well, the Permian Basin Regional Council of Governments. I don't believe there is a whole lot of crossing boundary lines when it comes to interoperability or cooperation (especially where money and grant funding is concerned). One of the questions we should ask is - Why doesn't the South Plains Association of Governments (SPAG) create a true regional system like the Panhandle Regional Planning Commission and the Permian Basin Regional Planning Commission?