What I ran into was that none of my ships, human-built or stolen from the aliens could possibly manage to get out of that massive beam weapon arc in time, and nothing short of the battlecruisers or battleships could even dent its shielding. Add in ships getting yoinked by its control attack and that when the beam weapon finally went off, everything except for the battleships vaporized, and I really didn't feel like going for the buildup necessary to make the battle work.
Hi, I made this game, so first: Thanks for playing it all the way through to the end!
Did you get to pick a bonus tech before the battle or did you go the alternate path (which ends at the "Project Backdoor" tech)? The second one is a
lot more difficult than the first and is basically a challenge path.
The easier route leads through
accepting the help of the alien defector when it happens.
If you go that way you get a pick of three ways to fight the battle, each giving a big bonus to one way of handling the fight. The fight is basically balanced for you using one of those options.
Also, as you noticed, fast ships are a necessity in that battle. If you scrap most of your slow ships at Earth, you get their resources back to build new ships with. That should be enough to build a specialized fleet for the final battle.
If it still doesn't work, please let me know where you stand resource and tech-wise. If you are in a weird spot balancing-wise I'd like to look at it; maybe I need to tweak something.
On a side-note: Half the feedback I get about boarding is that it's too weak, the other half tell me it's a bit OP. Must be about right then.