Quick strikes
Do a warp gate strike to stop reinforcements, after regrouping and resupplying do a command station strike to get rid of control and supply - make sure you have HEAVY defenses ready when you do that though.
If you can get most of the ships to come through and attack you (preferably via a wormhole you have well covered) send your fleet in with a FF - once the FF is through the wormhole, send in a few engineers to keep it alive and to help build a colony ship. Send through a mobile builder and immediately start construction of the colony ship.
With the Ion Cannon there I would suggest at least 6 Mk II engineers - 3 to focus on keeping the shield alive, the other 3 to keep the construction of the colony ship going. There are ships that are immune to the ion cannon strike I believe (not sure but maybe Raid Starships?) - send those in to help mop up on stragglers. Once you have your orbital command station built sit back and watch the carnage as the Ion Cannon mops up the enemies remaining
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Considering its a Mk IV world you will definitely lose many ships so try and go in with a min of Mk III as your vanguard for the strikes.
This is just a suggestion, and it may or may not work (the AI is frikkin sneaky at times).