Since pushback with engines running is not permitted, I set everything up at the gate using the GPU to power the plane, then disconnect the GPU, push back and do a battery-only start. After turning the avionics back on, I find that I have to turn the FMS back on and then re-initialize by inputting the departure location.The flight plan etc. is all there, so no big deal, but is this working as intended?

i assume that its permitted to get pushed backed by a pushback vehicle? Use the Reverser - JS41 can go backwards on its own - so you can start the engine while connected to ground power. that thing with the avionics was also strange to me, i just left it running while started the engines and was unable to take off (config error).