I don't know what to say to that Steve.
I fired the Kostura, watched it traverse the map... scrolled over to my Starbase, popped the ability (SPS) as soon as it was done upgrading to it, watched the Kostura shot impact the world about 4 seconds after that... scrolled back to the starbase and told my fleet to ship out about 6 seconds after the kostura shot hit (so we're talking 10 seconds after the impact)... and it gave me the aforementioned ass-backwards flightpath. I tried re-clicking it for the next 15-20 seconds trying to figure out why it wasn't working. Oh, and my fleet was on the edge of the grav well ready to rock - so travel time was not an issue.
The only thing I could think of is: Does the stabilize phase space ability spawn with the cooldown already ticking before you can use it? If so, maybe the icon just wasn't updating properly and I was in some sort of waiting period. Although, the graphic of the stabilizer was chillin' in the middle of the base (the swirling blue thing that you see inside the PS tactical structures).
I'll be firing up the game again later tonight and seeing exactly how many times I can get frustrated with this in a row to be sure that it's not a matter of my timing (or perhaps, is). Also, I'll see if the same happens when I tell a Marauder to stabilize phase space and see if the rest of a fleet can leave from there to a Kostura blasted target as well (just to be thorough).
PS: How often does the game, uhm, 'refresh' itself? This was happening pretty late in the game w/ two ai's and myself each using about 1000ish fleet supply, and there was a large battle going on, and a smaller battle at one of my star bases, and a large number of pirates were displaying their idiocy in one of my mine fields. Could things get busy enough where it didn't register the stabilized node before the Kostura sps effect expired? The game didn't seem to be acting sluggish or anything, so I'm assuming the answer is no?
PSS: And how long exactly does the Kostura shot stabilize the target for?