Took 15 minutes to "fix". But the player and other characters now actually move off the screen when they're on a warp trigger.
It's still stiff, as there's no walk in animation. But it works nicely so far. You can also see these rough maps have changed a bit. Mostly for flow and visual appeal reasons (as I tend to use the rough maps as a way to shape the final ones after some play-testing to see if they feel right to me)