The Advent player seems to be using the Progenitor to Shield Regenerate his Destra fleet and help them live longer, while imposing Malice on your fleet and doing more damage.
Once you have Transporters, their Fighters and Bombers can pretty much take over the Assailant's job of long-range Phase Missile assault, so you could maybe have 10-15 more Transporters and ~10 more Enforcers in place of those 40 Assailants. The Bombers, together with the Enforcers and the Evacuator's Nano-Disassembler should be able to bring down the enemy Progenitor.
As for the position of the Transporters themselves, they should stay in a seperate fleet as far back from the battle as possible while you try to make the enemy engage your Enforcers.
You should also tech the Distortion Field ability for the Subverters, allowing them to disable large chunks of the enemy Destra fleet for a while. The only problem is it's antimatter cost, which requires you to buy antimatter techs or else confine the ability to home ground.
As for those planet bombers, if you get your Evacuator(Space Egg) to Level 6, forget about 'em. Drain Planet will take over their role. Also, the Space Egg doesn't have a repair capability, but the Skirantra Carrier does have a Repair Cloud and the fugly Serevun Overseer has a 200 HP insta-repair ability. You can use either of them to repair your ships.