ATP has a Jax location at KCRG. At 1 point at hey were doing some 141 training out of that location but I don't know if they still do or what the deal was with it.
I would say that ATP would be a good bet if you're looking to go from zero to hero in the shortest amount of time. They don't have a 141 program in Jax but they do just a bit south in Daytona