From the LHR side of things (my mind is pretty much fried today so I can't remember the name of the mode you're in) there's always a way to get contact numbers: of the TRM/TRC/Dispatcher/Redcap/whatever name they pass under, of the gate and of the person in "closeouts", or FMU. I even remember finding the phone number of the baggage lateral for a particular flight once... and they replied! This is at least on FLY, I've never really used the JFE (although I know how it works behind the scenes!) so can't say about that.

I've never used FLY or PRS at an outstation, so I don't know what would happen there, although I do wonder who does the FMU-equivalent for the inbound and also who was being called every time I flew standby, the flight was looking dicey and they were deciding whether to give me a jumpseat or not...