Honestly, I want to keep the top down space combat, but make some major graphical additions, as well as add new features to the gameplay. At its core, the Star Control series's combat wasn't set up to be either RTS style, or 3D space simulation style. Star Control Classic's Melee is fundamentally a fighting game.
Fighters have come a long, LONG way since Star Control 2 came out in 1996. Star Control 1 actually came out in 1990, meaning that it actually predated Street Fighter, despite convergence in character / ship selection! In that time, fighters have added specials, supers, the ability to have multiple characters involved via tag-outs and assists, and a plethora of properties, movement options, and techniques. There is a lot of room, I think, to expand on Star Control Classic's Melee, as long as we keep in mind that, at it's core, it's a 2D fighter.
2D fighters focus on having a wide variety of characters with a unique and colorful designs, differing movement options, different character styles. Tactics revolve tremendously around positioning, movement ranges, speeds, styles, and controlling the opponent's psychology. Certain characters will have restricted movement options but tremendous damage, or unconventional movement abilities that make them unpredictable and dangerous.
I want to expound on this, but I don't want to bore everyone. Suffice it to say, I think that the 2D, top down, fighting game should remain, but additional things, such as limited count special moves, differing environmental hazards, option moves (like selected supers in some SF games), new odd movement styles, and potentially tag-outs or assist moves ought to be included. We ought to be able to have a tertiary ability, and possibly different classes of ships.
Fighters have already explored the ability to have one vs. multiple characters, with some success. In Skullgirls and Capcom vs. SNK 1 & 2, you could opt to pick fewer characters in exchange for a proportional boost to the damage and health of your choice. While I don't think we ought to have a proportional boost, I think that it would make sense to class ships into Scout, Cruiser, and Capital, and restrict the Squad size based around the classes. That would prevent, for example, a 6 on 6 battle between the Chenjesu and Shofixti ships, helping balance the cheaper ships with the heavier one, and encouraging a diversity of squad. Star Control 2's Hyper Melee approached this by its ship cost - this would just be a simplification.
I'm overflowing with ideas - I'd be glad to discuss 'em.