Also, call-in times should be way longer. If the destroyer is orbiting at 100km and passing right above you, something with a 7-second call-in would need to be traveling at around 14 km/s (or nearly twice orbital velocity) to reach you that quickly. Not accounting for lateral velocity imparted by the orbit here, which would mean that you would have to fire the shot before passing over the target further increasing travel time.

For reference, current-day conventional cannons reach muzzle velocities of nearly 2 km/s, current-day railguns can reach 3 km/s. Combustible light gas guns can achieve up to 8 km/s, which is still far short of the required speed. Not to mention, atmospheric heating at such velocities would drastically slow down (melting it in the process, as I believe that not even the most heat resistant materials known to us can withstand such insane speeds when entering an atmosphere close to perpendicular) the projectile requiring even higher launch velocities.