I think that GURPS is, in fact, right up your alley. It gives more agency in many ways than, arguably, most systems. In my experience, not being engaged or not having fun with the combat has as much to do with the narrator as much as it does with the mechanical options. The following is largely written about melee, but ranged also has similar options across the board.
I think that GURPS hits the mark for agency, intuition, and narration. Each round of combat is 1 second, so each participant does, effectively. First, the attacker needs to be good enough to even potentially hit the target. If the attacker can't hit the target because their skill is too low (they can't manage to roll under), nothing happens. You have options to make this better, including evaluation, which stacks as high as a +3 bonus for the next attack, and similar maneuvers. An all-out-attack (which does not allow you to defend that turn), has a number of maneuvers the attacker can use, like determined for a +4 to hit. By far, the greatest number of options are available for attacking, which helps to enable narration.
If the attacker makes a good enough roll to hit the target, the target has options, depending on the circumstances, to parry (one attack from one target each turn), to dodge, or to block with some shield or other object. Their respective rolls for those abilities are typically more difficult than attacking. Dodge uses the basic speed of the character, parry uses the skill of the parrying-weapon/2 +3. There are maneuvers an attacker can use to make the defenses less effective, like deceptive attacks, and feints. There's your agency.
If the defender fails the defense roll, then you roll for damage. Armor and shields, interposed material, etc, reduce damage. This is, in my opinion, much more satisfying than armor rules as given in most other games, ignoring unearthed arcana, which introduced a similar damage reduction value.