I think we're overthinking the status of the player. Yes by definition this BR is now just a runner because she reached first. But if defense is attempting to tag this runner now that she has left 1B then the runners base path is from her location at the time of the tag attempt directly back to 1B with three feet each side of that direct line. She has NO basepath back to home. So if she runs away from a tag attempt towards home plate (as a runner rather than a batter-runner) she is still out. But it would be like running out of basepath anywhere else: it's a liv ball out rather than a form of INT when a batter-runner retreats.
We're still getting an out. There will not be a run down.
