Dunno if any of you dudes have learned this already, but FYI, don't teleport to an instance with the LFG tool while on a flight path.
Unless you're 1337 like me and can click levitate/slowfall/parachute quick enough.
EDIT: So this setup happened again and while I was dismounted in the two seconds between when I accepted the invite and when I was ported, I was safely on the FP after I finished the run. I suppose this was either a very random bug or it was hotfixed.