I was an idiot. I said there was no good countertactic to fighting Eldar in the asteroids. I was wrong. There are several points to consider:
1) Asteroid fields are D3x5cm D3x5cm big. That's not much.
2) Put the field up sun of you, so that the Eldar ships will have to go back into the sun on their return trip back to their haven (should shorten their effective range a bit)
3) Go in after him. At least that way, he can't shoot you. Your shields will take the rock hits, and you can even launch attack craft. They have a chance of dying, but it's almost a guarantee that when you go in, he'll leave for another field or just leave. Just make sure he doesn't get around behind you once you run him out of one field. The bombers and other things will make life harder for him in the field, which will look small in no time.
--T. Ray