I hope Named helps with this, because addressing this challenge is at the core of what it does for us. Long before FKR existed or I had heard of Eisen’s Vow (players shouldn’t know the rules), we experimented with running D&D 3e with what we would now call ‘black box’ gaming (all the rules behind the screen) to try to better engage with the fictional world. Named is our evolution from that to something that makes staying in the fiction easy for us, but still has high impact rolls that change the direction of play.
I do think there are different balance points for people in staying in the fiction, so recommend you experiment around it to define your own balance using Named and any other tools that make sense.
All the best with your journey! Feel free to reach out if I can help.