People love to tell me how ineffective it is to kill Astro Train Stations, which I've never understood. That's a strategy that I use in all my games, and have since the game was early beta, and it works wonders. Not as well with a train master or similar, but in most games it doesn't take but a few hours before there are practically no trains coming through my systems.
At any rate, that's what I would do here, too. Simply snip off the astro train stations that are near yourself, or where you want to go, and that should help immensely. Astro Trains are only able to move from one station to another, so if there are no lines between stations that intersect your area, you won't see them. Then when the AI ships come into your area, you kill them once and for all and that's done with it. This is another reason I tend to carve out a corner of the map and then make my offensives out from there, is that then there's really no chance of that sort of thing. But it should be a strategy compatible with most styles of play, I think.
