So, before I get autoflushed into spam, I've had an idea.
What about trying to make a game with a three-minute start-to-finish combat turn (assuming, oh, 8 combatants). That's not three minutes of declaring and resolving actions; the goal is to have 33% mechanics time and 66% narration time. I also want it to have combat versatility with modifiable giant robots (and interesting but largely analogous personal-scale combat).
Here's what I've got so far:
Simultaneous turns: Actors get cards that they use to declare their actions; no need to verbally announce. You roll your dice, place your card, and move the dice onto the card, which has special spaces for special effects.
Single Rolls: There's no to-hit chance, every attack hits unless a defender manages to avoid it or block it entirely. Multiple dice may be used, but never in sequences: roll all of 'em at once [special weapon effects may actually be separate, but you could, say, use colored dice and roll simultaneously or roll extra dice separately].
Single Math Operations: No more than one math operation per actor. Preferably a total number of operations roughly equal to .75*Actors.
Limited Persistent Resources: We're not going to be tracking any changing numbers that we can't store on dice. Weapons have an ammunition count, for instance, but Ammunition is basically "Weapon does a bonus Xd6 starting at this value, rather than rolling the dice they start at a certain face value and are decreased by 1 for each subsequent attack." There are no hit points: mechs lose locomotion systems or weapons each time they get hit, while people lose arm/leg use. Fifth hit always incapacitates. Brutal weapons cause permanent damage, most weapons just take someone out for a combat. Mechs don't get incapacitated just by losing locomotion and weapons if they have spares, while people actually wind up going down after four hits. You can build some truly frightening giant robots, but even a twenty-limbed monstrosity still goes down after five successful hits, and its evasion pool falls pretty low.
Out of combat, I have a very simplified system for play, because I want this game to be novice-accessible. The roll system is somewhat inspired by D&D's Proficiency system, with a Attribute plus Skill rating that is then modified by an overall Renown rating, which provides d6 dice to roll. A "specialist" should have a A+S rating of 5 per die from Renown, while a "weak" character gets about 1.5 on average. At high levels, normal actions become reliable, but not guaranteed for characters who aren't specialists in the field, while specialists do epic feats like it's nothing.