Michael, I scripted a mission where a supply vessel accompanied you on a long range exploration in to a new sector. It entered the sector and then held position. The indicator on the science console changed to a base indicator (round circle). The ship then acted as a base, however it remained looking like the ship that had followed you in to the sector.
In the script, I actually destroyed the original vessel and created a base in the same position. By selecting the "TSN Transport" Hull ID rather than the base, I was able to keep the same ship, so when you docked it looked like you were linking up with the ship, not with a base.
You could do something similar, where the ship travels out to you. When it gets within 400m it switches to being a base and you simply initiate the dock. When you undock, the ship can then switch back to being a normal ship and head back to the original station. On the science console, the indicator would change, and if you watch it, the angle that the ship is facing will switch, but other than that, the ship would look the same. I think some embarrasing comms messages would be fun to add as well; something that highlights the fact that the most advanced ship with the "best" crew now needs rescuing!
Tre, feel free to repost the code. I have put the code on to the Wiki for people to access already though, and have included instruction on how it operates, as well as how to add it in to a mission.