No, in a way, you were right Anayar. You can't change a static entity to a dynamic one in a multiplayer map. What you can do however, is edit the entity's .fpe file.
When I thought about it again, I realised that if the lifts can be used in a multiplayer map, why can't the teleporters? So, I asked myself "What is it about a lift that makes it useable in a multiplayer map, even though it defaults to static?".
That's when I started to look at the .fpe files for the entities. I noticed that even though you can't edit them in the map editor, the .fpe files still point to certain scripts.
So I had a look in the scriptbank, to see what scripts made the lifts work. I found the 'transportifused.fpi' and the 'transporttoexit.fpi' scripts.
After that, it was simply a matter of editing the teleportIN.fpe file, in FPI Editpad, to use the 'transporttoexit.fpi' script!
I game therefore I am.