Ok, let's try this again.
I want a way for players to resolve their characters' actions that fits right in with the flow of the game/narrative. Despite how the last system came out, and the fact that it seemed fairly cool, I don't want a "minigame." I don't want something that creates a conflict arena and a non-conflict arena. D&D does that - you have to ask "Should I roll initiative?" and "Is this a short rest or are we still in combat rounds?" In SA, you should just be able to say "I'm going to shoot him" and have the numbers tell you whether you hit or not.
I want a system that lets multiple people collaborate on a course of action, with each of them contributing something significant to the final outcome as long as they're not completely outclassed.
I also want a system where someone with String 4 can clobber a whole gang of people with String 2, and someone with String 8 can clobber any number of String 2 people (with training making a difference, of course). This part may be better done with descriptors than numbers.
The rules should work equally well and equally smoothly for one-on-one, one-vs-all, team-vs-team, country-vs-country, any sort of conflict. It should all be "describe and compare numbers."
I want a small set of modifiers that can be used to help adjudicate tactical decisions. The GM should make a call as to whether a maneuver is a little helpful, a little harmful, particularly advantageous, etc. and be able to toss a few extra points one way or another.
I want people to be able to use many different resources in a conflict, but to need a strong finish with the right thing if they want to achieve a particular goal.
I want a difference between high-stakes and low-stakes conflicts. If you're racing your friend home from the barn, that's very different from racing the bomber to the reactor core, even if you're running your fastest in both cases. Achieving more significant consequences should feel more significant mechanically; perhaps a greater margin of success.
I want a way to have "subtle" conflicts, where one side either a: doesn't realize the stakes, or b: doesn't realize there's a conflict at all. If your character wants to bamboozle someone into thinking the race to the reactor room is a low-stakes contest, you need to win a subtle conflict first, which should provide the "significant feel" normally needed for a high-stakes conflict.
I will need to write guidance for the GM on how many adversaries should be included and how difficult they should be for a particular number of PCs, depending on whether the encounter is intended to be easy, tough, or overwhelming.
edited to add:
Timescale should still be important. You can't expect to interrupt mesh-hacking through psychohistorical manipulation. However, that's probably the sort of thing that can be left up to group/GM judgement.