Visit the concourse at a station with no shipyard then, without stopping anywhere else, dock on a fleet carrier and use its escape pod. You'll then be on foot at the shipyardless station I think, and able to test a Live Horizons login.
In this situation I believe the stuck recovery option (loth as I am to mention the dreaded Button) will put you back in your ship at the system where you left it on the FC, close to the main star, and I suspect but don't know that a Live Horizons login will do the same.
