What if Cannon Rapid Fire and Scatter Volley forced all of your cannon weapons into a cooldown mode after being fired? After the cannon effects expire, all of a ship's cannons go into cooldown mode, which will either:
a) Prevent all cannons from firing for 5 seconds
b) Severely reduce the amount of damage they deal for 5-10 seconds
The reason why I suggest adding a drawback to cannon abilities has precisely to do with the fact that they don't suffer from any in the first place, whereas beam abilities have some drawbacks associated with their use that may make them less desirable to use in some situations. Beam Fire At Will can provide higher overall DPS and multi-targeting, but doesn't let the player control how it fires; likewise, Beam Overload causes severe weapons power depletion and prevents any weapons of the same type from firing when the beam is armed.
By adding some sort of cooldown period at the end of Cannon abilities, it would add a similar disadvantage and not simply let them be a cheap and easy way to add considerable amounts of DPS, of which Escorts and Tactical captains have in abundance. In addition, it also might encourage escort captains to diversify their weapons mix into beams or torpedoes, because such weapons would remain affected.