My main concern with just a stabilizing tool is that it is not needed, and is sort of redundant. Turn off your engines and kick on moonshine, and you stop turning completely. Feather the throttle and balloon a bit, and being motionless is easy. Tiny thrusts of moonshine while turning, or using bumpers makes micro adjustments simple. These tools are also great if they start closing, or get to you.
Really, it is not even needed as a sniping aid. Sniping is pretty easy as it is, and I don't see making your easily stable platform even more stable as something anyone would need or use. Would it actually add much to sniping? Not really. No real benefit warranting replacing tools that are useful for stabilizing and combat/escape. It kinda seems like it would be an 'Easy Button' for pilots of sniper ships, which have a rather boring job as it is.
If you added the gun dampening feature, it would not help the long range guns at all, since they have little to no recoil. The ship stabilization would help some at long range, but not really enough to warrant bringing it. That would put it right in the mid-range, high reward, high risk area of combat. Mid-range because of the heavy-ish gun dampening. High reward because of the improved hit chance of mid-short range guns with higher recoil, and use of higher damage ammo. High risk due to the sacrifice of combat and evasive tools, and that you will actually damage your own ship if you even try to evade during the release cooldown (lasts X seconds after tool is deactivated).
Let's take the example of the dual hwacha, gatling Galleon. Mid range disable, close range kill build. It is also easy to close on with fast ships, easy to snipe out with long range builds, and easy to kill with mid-range builds. These things can be overcome with other pilot tools to some extent. Using the stabilizing/dampening tool would change the behavior of your ship quite a bit. Yes, you could get rid of your gunner, but I would not, for the following reasons.
1. Lesmok would actually have a use in the hwacha, and be far more useful in the gatling. You can get an increased rate of disable at the extent of the hwacha range, almost being able to contend with most sniper builds. You can also get more accurate shots at mid range on rapidly moving ships.
2. You don't want to only have lesmok. That makes a gunner necessary already on any hwacha/dampened ship.
3. Incendiary would be much more useful making it a more viable ammo. Most of the time if it is brought, it is the third "What else should I bring?" "Don't care. Incend if you want", just used if the enemy ship is already crippled ammo. This would make it more viable as an offensive ammo at max close range. You would no longer load hwachas and carros with incend for the lulz. With spit second coordination between pilot and gunner, it would prove greatly effective. At max incend range, the pilot orders the ammo loaded, kicks in the gyros, takes some armor damage as the ship shudders to a halt, and orders the barrage. Of course, a poorly done maneuver like this will end with your ship immobilized and vulnerable.
4. Burst, of course. What is not to like about more burst shots hitting?
5. Heavy clip. Still needed as the go-to first contact ammo choice. Even better with the dampers bringing the ship to a screeching halt right before you fire.
In short, I think this tool would make a gunner far more effective with an increased number of viable ammo types.
The big con, of course, is that any time you do use it, your ship is almost completely immobilized, much worse than using bumpers or chute, and takes damage if you try to adjust. The effect would last for several seconds after you stop using it as your gyros spun down. Perhaps the gun dampening would only last while the tool was in active mode, removing the cooldown time as part of the beneficial 'heavy-like' gunning period.
A lesser con is that it would only help much on guns with recoil. It would help some with long range braking after repositioning, but moonshine is a much more viable tool when it comes to bringing your sniper ship's rotation to an instant halt.
I feel that these things would make the tool a balanced offensive, crippling defensive tool, which I feel are lacking in the pilot's arsenal. There would always be some risk in turning it on, and would entirely depend on your piloting preferences. Using it correctly at just the right time would be devastating to your foes. Misjudging the timing would mean certain defeat.