This is a bit of a necro, but I wanted to share an easy (and very fast) way to beat this mission in case others are still having trouble.
I'm playing with everything patched up to the latest versions and on Normal difficulty. I haven't tried it on other difficulties.
For abilities, I recommend getting Creativity, the first level of Speed, and then whatever else you can into Soldiering. I don't think even all that's necessary, though.
When you start, set your anomaly ship to Auto Survey. It will provide you with some goodies while you rush through the mission. Send your Constructor up towards the target planet and build a starbase at the edge of the Constructor's range when it gets there. It doesn't matter what kind, you just want the extended range. And send the scout ship up towards the target planet.
Start building on your planets, but buy the first couple buildings. I like to buy a Factory and Research Lab, then build the Recruitment Center (or buy it if you want). Set the production spending (or whatever it's called) to 100% and set your taxes down towards 15%, or whatever will get you 100% happiness. Start researching Antigravity, and once that's done, start researching Planetary Defense.
Buy a Colony Ship and send it up towards the planet closest to the target planet (off to the right of it). I don't believe this step is necessary, but I do it anyway to make sure I have the range along with the starbase. I just set the slider to 25 when launching it, as I don't intend to do anything on this planet.
After you've progressed through a few turns, speak to each of the races and see what ships they have. Two of the races will get 4-5 frigates each. Try trading your treaties, new technologies, and any reasonable amount of money for them. See if you can get the third race's ships, too. It may take a number of turns, so keep checking.
Once you get a large number of the ships, immediately send them up towards the target planet. You can buy a Battle Axe or two if you want, but it's probably not necessary.
Buy two transports at your homeworld. You should only need one, but two just to be safe. Send them up towards the target planet with full troop compliments.
By now you should have a large number of ships moving towards the target planet. Hopefully as you do this, your Creativity ability will let you finish Planetary Defense ahead of schedule (if not, don't worry). Keep checking the other races, as they'll replace their frigates and you can often get more.
You should be able to see the DL planet with your scout ship, so keep an eye on what they have in orbit. If you're really fast (or maybe lucky), only Sarak will be there. In that case, all these ships aren't necessary and you can just use one and a transport to win. If they have a real defender, though, you'll be glad you have all those ships from the other races.
At the very worst you'll only have one defender and Sarak to deal with. With all those frigates, it won't be an issue. Wipe out what they have by sending them in one by one to chip away at the defender. Eventually you'll kill it and Sarak, then invade with your troops. Pay for Gas Warfare to give you better chances and hopefully it only takes one transport. If not, that's why you have two.
Congrats, you just beat the mission!
To sum up, extend your range to the DL planet immediately and barter for the other races' frigates when you can. Buy yourself a couple troop transports and send everyone up to the DL planet. Win.