I love HuntingU's idea of you controlling a small "Drox Guild" instead of just one ship. That could be a cool differentiating feature from the original. A lot of people, myself included, really enjoy having persistent bonuses and upgrades unlocked, so that could play in well. (Persistent in this case would be to the character/guild, not to all characters in your local installation -- start a new character/guild, start with a blank slate. But obviously the gameplay loop is running that character through many systems/games, so this makes sense.) Perhaps that persistence is a skill tree which you have to make choices in rather than being able to unlock everything -- hard choices and specialization are fun!
Huge boss ships/special encounters would be great. I can imaging having to fly around a ship/base that is 2 or three screens huge, taking out defenses all the way around it bit by bit in order to be able to attack it, or as mentioned, have different phases, or repeatedly finding the weak spot as the enemy beefs up defenses where you have been attacking it... there's a lot of cool things that could be done here. Especially if we make a pool of these things that can be caused from a variety of actions, and have different modifiers that make each instance a slightly unique experience -- affixes beyond just numbers and resistances, but optional mechanics, different phase order, etc.
Perhaps the Command Point system could be redesigned, or dropped altogether and instead you bought and upgraded ships in a different manner. Or Command Points were like a currency instead of a sequential upgrade, and you had access to a shipyard where you could use that smaller, earlier ship but buff it to make it viable at any point. Being able to invest in "weaker" ships to make them more powerful is a great way to really personalize things. Options are good!
Can you tell I'm excited?