Ok I've not actually had chance to test this as of yet but as far as im aware it should be doable, I've been doing similar things in the Distant Stars mod, and this one an idea I had toyed with introducing at a later date.
First things first, you'll need to create:
- A new Frigate class vessel to spawn the ship from, or atleast a copy and paste of an old frigate
- The new frigate needs a new ability, lets call it "AbilityNeutralStarbaseSpawner" for now
- The new ability must auto cast upon the ships spawning in a neutral gravity well, so i'd suggest setting the skill to passive so it can't not spawn the starbase.
- Now comes the tricky part: If the starbase is causing a minidump in this form its due to it not being "owned" and it will need to be spawned for a race, specifically you'll need to add in a new "sub-race" or use an existing sub-race referenced within the GalaxyScenarioDef file (near the bottom)
- If you're still encountering issues like this (you shouldnt do due to starbases being able to be spawned in any gravity well), the ownership isnt taking effect and will need the planet/neutral sector to be owned by the same sub-race your obviously spawning it for
- To make the starbase capturable you'll need to add a buff to it (or edit a buff, i'd suggest creating a new Destabilize Hyperspace ability and adding in the captureable tag to it (duplicate the previous and add in a new buff)) depending on how you want to do this you can either make it a one time capture, permanent capture, or a timed window where it is re-capturable. You could also make the capturing ability "channeled", your choice 
Also a big important note here: The starbases are very very fickle in spawning for specific races, so make sure the race that owns the starbase spawner, is referencing the correct sub-race, for example dont go trying to spawn a Vasari Starbase via the ability (starBaseType "StarBasePhase") and reference the TECH sub-race, this will I can almost guarantee cause an instant-minidump.
Hope this helps, oh and dont forget to add the appropriate files in to the manifests.
