I am not based out of Greer, but I can tell you where you are based insofar as your "home terminal" has little to do with your miles. As a Swift flatbedder, I can say that if you are willing to run (especially all 48 states) and also smart enough to help out your DM/planners on the occasional "undesirable" load, you should have no trouble getting consistent miles. Your planners will be wherever you are at the moment. I.e. if you are in Indiana, Ohio, etc, Gary planners will do you. If you are in Washington, it is either Phoenix or SLC planner, not sure which. And so forth. Hope that helps.
Don't know if this has changed since those ancient days of me running flats for them, but it at least used to be that, if you ran out of the two East Coast terminals (at the time, they were Greer and Eden, NC), you'd typically be pulling stepdecks to PA, IN, MI, or IA, and they'd rush to get you back. Freightliner Custom Chassis was (and apparently still is) a major contract, and since only the east coast flatbedders were required to carry 20 chains and binders (for the five chassis loads to Utilimaster), planners didn't want to let them stray too far away. Which isn't to say that we never did, but we tended to be kept on a much shorter leash than the Phoenix, Gary, or Shoals flatbedders (aside from those who pulled covered wagons out of Gary and Shoals, anyhow).
I run van outta Gary but some of the flatbedders there I have talked to say they run the triangle. Steel coil out of Gary to Lardeo (going to Mexico), Finished stuff going to Freightliner in Greer, then the chaissis that was mentioned out to the midwest. Kinda makes sense to have the Greer guys do the same kinda thing but who knows.
The 'triangle' wasn't my experience with them. The chassis loads were high priority, so it would more often be a chassis load somewhere, steel coil stock back. OR, if I ended up in Georgia, the fun run - Blue Bird bus chassis from Fort Valley, GA to Brantford, ON (yep, that's Canada). And if you get that run, expect to be running back and forth between Brantford and the New Boston terminal at least a couple times - all the drivers who've had DUIs, missed child support payments, and other things which are felonies in Canada would T-call their loads in New Boston, and they'd need drivers who could go into Canada to take those. But again, a lot could have changed in the time since.