Thinking on it overnight, I'm wondering if I might be getting thrown sideways because it's the defender pulling the cards, so attacking feels like a very passive action. There's no strategy or intention behind the attack, it's just pull the trigger and hope, and then the defender gets to ultimately decide what happens.
You mentioned having special damage effects on some of the cards as an extra "bonus" bit of damage, but I wonder if that might be better served by pulling it out into a separate mechanic that the attacker is in control of. Just thinking as I type, so this may or may not work... but something along the lines of, each player is dealt two special effect cards that they can play with an attack, so say...
I move to attack Boter's ship, I have 2 guns, and I really want to blow out his propulsion system so he's a sitting duck. I play my special ability card at the beginning of the attack that says if Boter pulls a propulsion system damage card it auto crits. And just extend that to whatever other effects you can think of: If the defender takes damage to it's weapon systems from the attack, one gun is out of commission for a round. Player then draws back up to 2 cards, and can burn resources to scrap their current hand and redraw.
At that point, it's still effectively up to whatever the defender pulls, but as the attacker I can control a small amount of the strategy of the fight with what I'm (effectively) targeting that could have larger repercussions down the line, ie. I manage to crit Boter's propulsion, he's a sitting duck for a round, allowing me to move a second ship into firing range, but then Boter manages to get a shot into my weapons systems meaning I don't have the firepower to blow him out of the sky while he repairs his engines.