Check the frequencies used along the ARTCC boundary for ZTL, ZMA, and ZDC. In cases like this, they would keep the aircraft on their frequency and extend the ARTCC boundary to cover the loss of ZJX. That should be part of the LOAs they have in place.
Similar happened when ZLA had to evacuate due to wildfires. ZOA, ZAB, and ZLC have LOAs in place to handle the traffic until they can be handed off to SBA, SCT, or L30 TRACONs.
BL.