You might. Just drop another gaming convention left over from the earliest days of D&D, the combat round. Ringworld had a combat system solely based on strike ranks (ok, very short combat rounds, several of which are used to make up an action), and people just knew how long the action they declared would take.
I haven't ever played Ringworld, or read it, but I tried to come up with a similar action point or strike rank based round system myself. If you allow actions for either hand, or both in coordination, and another one for the entire body (including walking, kicking, dodging), you get a system where you can play combat to any detail you would want. And, like in Bushido, you could keep the other round based combat system for fights where minutiae don't matter. (And possibly include a d10 based, goonquest or Warhamster Battle-like system for fights where even time advantages etc. don't matter.)
Speed should be a matter of natural quickness, skill, and inertia of tools or body parts used.
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