apparently the bigger threat to the A10 was flame-out of the engines due to the exhaust from the gun depriving them of oxygen. This had happened while in testing and so they had to add internal igniters to the engine that fire when the gun is fired to keep the engines burning.
so the idea is you send the platform towards the target from long distance to keep yourself safe. it is primarily un-powered and just coasting so the enemy can't detect additional heat or radiation from your thrusters to give away that the platform is coming. when it gets close it swivels with the gyros to correct any aim towards the target, which may have moved since you sent the platform, but hopefully now you are much closer to the target, and they have much less time to react. It then fires its gun. if the target is directly in front of you, then using your math you get a good about 1k shots off before you stop relative to the target. however even after that the velocity of your rounds are still sufficient to cause damage, and maybe you can fire an additional 500 rounds that are still lethal. the last of which would be traveling around 500m/s towards the target, of course this is all ignoring the loss of weight due to the ammo being fired
even if the target is directly to your side relative to your direction of movement you can probably get a good 500 shots off towards it at potentially lethal velocity. if on the other hand you have passed the target before you fire, then it is too late and there is possibly no point in firing as your rounds would not reach the target. so you just need to make sure you fire before this.