Verticality can remain relevant and important with Shove being a normal attack-replacing action instead of a BA. Shoving an enemy off a cliff deals damage to them, sends them to low ground where you get a slight bonus to attack, and can require the enemy to spend turns climbing back up. That is well worth losing out on a single attack. Additionally, other classes can still shove characters via Thunderwave, Monk's Way of Open Hands shoves, and the Shield Master feat; letting shove be a BA weakens those spells/abilities/feats.
The most important mechanic necessary for Shove being an attack-replacing action is that of ladders&climbing. Ladders should cost (double) movement, and perhaps enemies should be unable to get on/off a ladder if an enemy is blocking the entrance/exit space. This would ensure that a shove gains you an entire turn - likely multiple - where the enemy is only moving back up to high ground. This would open up tactical options much more interesting and impactful than "Shove enemy dealing ~4 damage -> enemy climbs back up using ~0 movement and attacks you -> shove enemy again."
