Has FedEx started calling people? What is the status of the pool?
One concern with kids in tow is the location of Pilot bases. Are junior Fed Ex pilots still getting Guangzhou? It looked a little like China, then Anchorage, might be in the first decade of a pilot's career. Back when I was looking at FedEx pretty hard (2007) there were complaints that school for the kiddos was very expensive outside the US.
Another consideration is the diversity of FedEx's fleet. The 737 is a fine airplane, but cramped, loud, and just isn't as nice a flying airplane as Boeing's larger jets. (Have no bus experience to compare to) I'd not be happy with a whole career of 737 flying, but that's me.
Fed Ex has a really good culture among the pilots ... a lot of good people there. System Chief Pilot is a good guy.
Another consideration, a "bad year" for FedEx usually means more profit than an excellent year at a passenger carrier. SWA has been VERY well managed and does better than most of the pax outfits, but, the revenue model in cargo and high value cargo has superior long term prospects.
Be happy with Fed Ex or SWA, both are excellent companies.