Core fields are immune to EMPs and if i remember correctly, Eye is immune to blade attacks... sO maybe its possible to make small raids of like 200 ships (transported) and destroy it eventually? Sure, it will take some time, but this might work if there are no heavy defenses arround, and if there is, maybe you want to destroy those defenses first....
In the game i finished recently, i have discovered sth interesting... from previous version of this game the idea was to have as large fleet as possible so you have enough 'muscle' to take out the core planet. What i did in recent game was completely different - i was sending only small groups of ships 200-500 to destroy all core guardposts (transported, so they make it to destination lol), rebuild - repeat. If economy is at least moderate, it shouldnt be hard. Sure, i had advanced factory captured, but i'm sure it only gave me some advantage staying alive... So after all those core posts were destroyed, i got a headache trying to figure how to destroy AI comand station which was surounded by 2 core forcefields, when i suddenly noticed that comand station isnt immune to blade attacks and at that moment i had like 800 shreders, well you get the point
I am not sure what exactly your situation is, but maybe this gives you some ideas