Thanks for the suggestions!
For what it's worth, I have always felt combat/damage resolution was a potential weak point in the game engine.
Don't get me wrong: the To-Hit => Shield Roll => Damage progression is pretty much what makes Starmada, you know, STARMADA. And in the early iterations of the game, that was it, and it worked fine: one, two, three, DONE.
The problem has always come in when attempting to evenly distribute damage to weapons, which is when I added the fourth roll (sometimes) in Admiralty -- i.e. the weapon location roll. That, IMHO, became a bit cumbersome, especially when you look at some of the additional rolls that come in to play with certain weapon traits. And when I played the game, I felt there was too much down-time while my opponent resolved his attacks. (As a result, I may have allowed the pendulum to swing too far the other direction with Nova, but that's another story.)
Anyway, looking at your options:
1) The D20 roll is not a bad idea, but it does require switching dice in the middle of the process. With the D6 only method, you may re-roll a lot, but at least you're always picking up dice that are already in front of you.
2) I like the dice-less damage thing. Would you track for each individual ship, or for the battle as a whole? i.e. you attack me, and score three points of damage, so I check off one Hull+Engine, one Engine, and one Hull+Shield. When I attack you, do I start over at Point #1, or do I start at Point #4?