They can FCS after each attack... it's in the FAQ.
Though it may talk about Vader in the FAQ item. But if Vader can be used after each attack, I can't see any reason why your couldn't use FCS after each attack.
Q: If a ship attacks twice through some effect, such as the Gunner upgrade, can the ship
use the ability of Darth Vader (the Upgrade card) twice?
A: Yes, once after each attack
It's all about the comma. The timing for Gunner is "After Attacking" the
immediately
is not in the timing part of the card it is after the comma so is part of the card effect. Only once you choose to resolve it do you immediately start a new attack. But you can resolve other cards that happen "After Attacking" first.