The way I conquered this map was the following:
First, send out that Anor cruiser to kill all the Yor fleets you find, then continually have it fly around and kill any new creations (watch for the shield that appears next to the planet).
For your research tree, first set your two planets to 'focus - research', then research Stellar Category, Lasar 1 (and preferably 2), then Planetary invasion. After which, try "logistics" so you can send two transports instead of one at a time, or Planetary Bombardment to help with the invasion. Your Anor crusier is your bread and butter in this mission.
Also note to capture the resource fields, and upgrade them with the +1 all stats, at 200 BC cost. You'll be surprised how many Yor fighters try to take it down only to die. As a precaution, take the fast repair rate civ perk before the mission starts - this really will help your resource SBs survive, and gain levels of HP.
Once you've captured a few Yor worlds, it's all downhill - just crank out the Transport ships in one planet and perhaps some phonex mk2 or higher ships in your other world. This mission takes a long time, but it's not exactly challenging, just onerous.
P.S:
It WILL take a while to research planetary invasion - I had to wait 40 turns for it to happen. You don't have the research points in this map for it to take much less, so don't worry. It's probably an hour long mission.