Mines would make for a nasty surprise, but you'll need an extra turn to launch them
If you can get 24 mines in orbit, you can expect about half of his ships to be hit, and half of those badly hurt.
You could try doing some quick research into planetary weapons (napalm). If you wipe out the planets, his ships will crumble on their own. With napalm, you should be able to do suicide runs on the colonies, taking out the population before the defenses can fry your ship. A heavily armored decoy ship (must have some guns) plus a bunch of Napalm Escorts would probably work the first time, but your opponent would quickly change his strategy to target the smaller ships first. You can then reverse the tactic, and catch him again.
