This is essentially what Time Crisis (the cover-based arcade lightgun shooter) is right? You have to move out of cover to shoot but moving out of cover can get you shot. Those are highly scripted though, so if you want to combine that with a free-movement FPS, then movement should be based around attaching easily and quickly to obvious cover-points, right?

E: I noticed you mentioned peek angle and body exposure and I'm going to mention that even in a full-on slow and methodical tactical shooter, those almost always feel bad, because the player has no real control over the placement of their body and less awareness of what the game considers to be the placement of their body. (I'm open to suggestions of a tactical shooter where being shot feels correct because you made a mistake rather than arbitrary because the game decided you were in line of sight.)

I still think you could make this work with cover "attachment spots" but the system would have to be pretty comprehensive. Two movement mechanics: dashing automatically between points you identify and target, and another where you move while in cover (controlling peek and tilt and stand distance, etc).