Okay, we are going to have to talk Drone combat strats here, because fighting the Drone can be a big make or break of a run.
The first obvious talking point is that the Drone tries to evade missiles. This can be used to reduce its chances to fire on you and some of the AI evasive patterns are to just afterburn in a straight line and out run the missile. In my 2hr16min run this is the kind of pattern it seemed the Drone was using.
Something that I'm considering right now is how the Confed ships factor into the Drone behavior during the fight. Again, in my 2hr16min run you don't see the Confed attacking at all (you do hear some gunfire, and maybe they did fire a missile or two). The Drone's evasive AI could be negatively affected by proximity to the Confed as they attack it, so a calmer Drone could be a Drone that's engaged and lured away from the Confed ships.
Just some thoughts, clearly we need to practice the Drone a lot and try find some patterns.