The good news is bro... colony pods work quite well at stars. It's not as awesome as trade ports, but it's better than nothing. Furthermore, my starbase's trade ports worked fine on planets. However, they do not work on stars - and that is across all star bases of all races currently.
Just so you know: phase stabilizers do not work at stars either. So if you're thinking it'd be sick to 1 jump your ships to a star from anywhere in the system? Nuh-uh. Not gonna happen. You cannot phase stabilize a star - not with a base, an Antorak, or a Kostura.
As a suggestion, don't neglect colony pods. If you put even just one point into them on every non-frontline starbase you have, the cash adds up, and if you put in two points, it's actually quite noticeable - it helps. Where as I have found trade ports on an orkulus are only useful if you're trying to make a really long chain and need a port in a non colonizeable grav well.
-Itharus