Thanks for pinging me on this!

https://www.openstreetmap.org/changeset/131945023

I've gone ahead and just made a separate way for Burger King, since it takes the entirety of the first floor. The second floor is a disused gallery of some kind, as can be seen in Mapillary.
I've added two entrance nodes, one "entrance=main" and the other just "entrance=yes", and I've made sure it connects to the Burger King way, but not the disused gallery.

I think your solution of centering the POI node is also a reasonable one, and probably easier to maintain than how I added separate ways. However, by using ways we can mark entrances as belonging to certain POIs but not others.

Let me know if you have any concerns, or you can also change it if you'd like.