If you don't mind a bit of DIY you can use the IKea design system (available online) for closet organizers. You will have to pick the material up in either Orlando or Tampa. Cost will be about 25% of other installed systems.

Has anyone found a full service closet design company that pulls the wire systems, patches and paints, and then installs the new system?

I went to one and taking out the old closet was included only if they took it out the same day. So if I want the closets to look new and not dingy I need to hire a handy man to dismantle the old system, hire a painter to patch and paint, and then have the closet company come in and assemble the new closet.

Perhaps I’m looking for a closet general contractor?

Inspired Closets did all of that for us. Excellent design and installation teams. Perhaps not as inexpensive as some, but total delightful turnkey. I'd prefer to pay a little more...