what is your point? if you have gyros to control orientation and aim you probably have computers and some sensors to aim. the gun platform is now much closer to the target than the original ship from where you had launched it, so it should also be much easier to hit the target now. the target will also have less time to react to the projectile and move out of the way now.
but to fire projectiles at a moving target you have to fire ahead of it so the projectiles and the target meet.
this is already a solved problem. we already do it on earth with patriot missile system. and some of the targets they take down are moving faster than they do.
the amount of thrust used to fire the projectiles that way will push your gun and whatever it's mounted to, backward with the exact same force.
umm...so you mean just like you see in the movies where the guy shooting the gun gets thrown across the room, just like the guy he shot at?
the gun platform will already have velocity towards the target. all it is doing is getting in closer to the intended target, correcting the aim, and then shooting a projectile smaller than itself. (bonus points if the platform itself also hits the target, but this isn't needed). yes there will be some kickback when you fire, but it doesn't necessarily matter since you don't care if the platform itself hits. you already have velocity towards the target any more you can add to the projectile is a bonus. in addition you could either add extra mass to the platform to help counteract this kick, or add rockets to it that fire off just before you fire the projectile so that you can impart the most velocity possible into the projectile towards the target.
and actually it might be good to calculate the charge so that once the projectile is fired, it takes all forward momentum away from the gun platform relative to the target and parks it right in front of the enemy, just being a nuisance in their way. though you would probably want to fry the electronics so they can't easily reload it and send it back.