I had no idea they could move, that's a pretty bad idea IMO. I'd prefer to see immoble SP's with weapon systems. An SP really shouldn't be mobile. Unless you tug it with some huge tug boat ship. But moving on their own makes in not really a port, but a huge ship.
Maybe when you build them, you could choose the tile they end up in...? That might work.
And with no weapons, what's to stop even the smallest ship from destroying them easily?
I too don't like the idea of mobile star ports.
Choose the tile to build it in, within X tiles from the constructing planet.
Don't give it weapons by default, just give the option of building basic defensive weapons with a maintenance cost if built.
If you need to put in a better location, decommission it and build another.
Long term protection will require a docked defence fleet.