Which is why this won’t work as you’re hoping - it was intended as a leading question. You’re in for a fun one.
Only way I know to do this is to get each room out of the linked model, get each door’s location (a point) and offset it by a bit more than the thickness of its’s host element and the inverse of that value along the door’s facing vector. Next run a test to see which room contains which points, filter the list of all rooms by that series of masks, and then get your name and number (and whatever else you may want) for each room. Now you should be able to set each door’s parameter values accordingly.
Hopefully you have studied up on lacing, list levels, type vs instance documents, and getting elements from linked models.
Alternatively you could put thing into one model. Coping the rooms between models may be an easier morbid here, and would allow better scheduling by room for other categories as well.