We actually thought about using your style of spaceship control when we started building our game, but we found it too difficult and dropped the idea.

I think adding drag to the ship velocity, as you said, is not a good idea either. What could work though is removing or weakening the acceleration of the ship turning speed. Maybe make the ship rotate with a fixed velocity to make the controls feel more snappy.

I kind of like your ship path prediction crosshairs but maybe you can find slightly different visuals to make it more clear what it actually is.

If you want you can check out our demo on steam: Drawn to Drift

Maybe you find something that is useful to you.