I think the thing that got me out of that zone most was learning to play ska, actually. You can use barre chords and just tilt your hand towards the high strings to get the upper voicings, or you can just learn the upper voicings separately, but the bigger thing is that in order to get the feel right, you need to feel the downbeat and play the upbeat: swing the hand down like you’re going to hit it on the downbeat, but miss, and hit it on the upstroke instead. Seems simple, but is surprisingly hard to really lock in. And once you do, the basic ability to lock in the rhythm hand really tight is very transferable to other styles.