As someone who mostly defends against phase ships my main issue with the short cooldown (especially with the skill) is that I can't train my weapons at the phase ship and shoot it when it surfaces, I have to keep shooting at it in case it surfaces because the travel time of most attacks is too slow to get there before the cooldown is up and the ship phases again (until it overcommits and ends up with too much flux to get out of weapon range). That makes phase vs shield ship fights mostly about whether the phase ship's pilot makes a mistake, not what the shield ship's pilot does.
Yeah, just giving a cooldown penalty based on flux or even just a flat penalty won't really make it more interactive, it'll just mean that you might get to save a bit of weapon flux by not having to shoot until you can actually hit the enemy or you get to do more damage when the phase ship makes a mistake. With shields you have a game between the attacker and defender of which weapons to use, when to drop or raise shields, which way to point them, etc but with phase ships you can just saturate the area with bullets and hope the phase ship screws up and eats some of them.
Maybe it should be possible to hit some tiny part of the phase ship while it's phased to build up extra flux on it? Would probably be difficult to balance but at least give the shield ships a way of forcing a phase ship out of cloak.
The alternative idea would always be phase depth charges, something to throw out as obstacles for approaching phase ships.