How about this idea?
The FSD can teleport humans exceptional distances. However, in order to do anything meaningful (and, in fact, to survive) said humans need life support, materials, resources and tools. This means vessels, which weigh a lot more than a human. As a result of this fact, the FSD has a massively reduced range (but usable as we can 'fly' ships with cargo, passengers and other materials). However, the FSD ALWAYS (even when 'destroyed') has the ability to teleport the pilot (of the vessel the FSD is fitted to) back to the last station the ship docked at (as the FSD systems will record the co-ordinates of that station as it docks there). The REMlock systems (which help the FSD to focus) will protect the pilot during this 'jump', holding them in stasis until the station medical bay shuts down the REMlock suit.
This may be reasonably possible. If we consider that an A Rated FSD can drive an Anaconda over 20LY (and this ship weighs over 1,000 tonnes when fully fitted out, not including the cargo) the same FSD ought to be able to propel a human (which, for the sake of arguement, weighs 100KG wearing the ship-suit) 200,000LY (OK, this has to rely upon the destination station rescuing the 'castaway' when they 'jump' into the vicinity.