Old Is Gold
..and..
In short: When in doubt.. beachhead it.
EDIT: OK OK..... I can't resist trying help and giving more detailed information... I was trying to be lazy but nope I can't do it. That's not me.. not but rly.. I like it when people ask questions/help and strategic tips and stuff. It helps me think about stuff and keep writing my guide to AI War.. which is the only AI War guide out there.
If you uploaded the save file I could take a look at it.
the reinforcing AI ships
I assume you're talking about Special Force and/or Core Reserve ships. I have 2 counters to those. The other one is tested and the other one is a theory.
The first (tested and works for sure) one is kiting around with Riot Starships. Preferably Mark III Riots. Group move around the planet and let Riots destroy their engines so they become sitting ducks and are scattered around the planet.
And the second one is building a Mark II Gravitational Turret beachhead to clump up the AI ships and then blow them up with a Mark I Lightning Warhead. Instead of using Warheads you can also try building Area and EMP Minefields. If you're going to use Warheads make sure they're always cloaked by Cloaker Starships. Otherwise they will blow up accidentally.
You can also combine the first and the second one: Mark III Riots + Mark II Gravitational Turrets + Minefields.
The question is how would you actually do those^^ well..
..here is an example of offensive beachheading
Gravitational BeachheadA normal beachhead like that^^ would get destroyed by Special Forces and Core Reserves though. So you would probably have to build multiple smaller beachheads. Most likely consisting of Gravitational, Missile and Sniper Turrets. You would have to build multiple gravitational "bumpers" or "walls" and kite the AI ships so they have to go trough the Gravitational Turrets. Then they will clump up and you can blow them up with a Warhead. While the AI ships are working their way trough the Grav Turrets your Riot Starships, Missile and Sniper Turrets will do their thing. Spider Turrets would help a lot in this case. You can also combine Grav Turrets with Tractor Beam Turrets.. and the minefields of course.
In my current game I will soon attack the AI Homeworlds. Then I'll try this Gravitational Beachhead or something similar to it. If it works I will take screenshots of it.