Good summary, but I don't agree it was refused landing at IAD unless someone has ATC recordings. Touch and Gos are common for mil aircraft . Agree it was probably refueled in CLT. I was listening to MSY tower in New Orleans. There was no request to land at MSY. GAF689 subsequently flew to JAX where it did land.
On the attached graphics the "dots" are ADB info locations. The areas with no dots, e.g. between Hattiesburg LA and off the LA coast was the area where there was no ADB transponder info.
My theory on the indirect route to JAX was to throw off anyone tracking the aircraft. We thought it was going to IAH or MSY. JAX was a litteral curve ball, but one that makes sense as JAX is a known staging and transport airport for GITMO. There are regular charter flights daily / weekly from JAX to GITMO