In built particles can be useful and save some developing time, once you know them, however they are kind of limited, yes:
Quote: "fade particle colours/alpha over life of individual particle"
Not possible, all fade at once.
Quote: "Create a new particle emitter per single particle and manually scroll colour/ghost for each?"
I don't think so either.
Quote: "-set particle acceleration in 3 dimensions
-set initial particle velocity (trajectory) in 3 dimensions"
They work as you stated, however the particles can be pointed.
Quote: "create my own system for moving particles manually in other directions?"
That's the way for refinated particle paths. Standard particles could be pointed in one direction or another, all at once.
Quote: "- specify number of particles for trails"
Not really. Only way is with Set Particle Emmissions function.
Quote: "Ditch the existing particle system entirely and start from scratch using sprites manually?"
Yes, it seems that you have enough reasons. Use sprites or 3d instanced planes pointed to the camera, depending on your needs
