I don't think TMP includes the direct object of the sentence, which 'das Krankenhaus' is in this case.

I'm not a native so please correct me if I'm wrong but as I was taught it, TMP in German mostly relates to adverbial phrases and prepositional phrases. So, if 'das Krankenhaus' were part of a prepositional phrase, it would of course be as you said. If the sentence were something like 'Sie wird (heute,als Patient, usw.) ins Krankenhaus gehen', then you would need to pay attention to the position of where the Place phrase is relative to those of Time and Manner.

I wonder if since bald is modifying verlassen, that it has to be "close" to verlassen instead of wird