Is "back the hall" accepted usage?

No, that isn't grammatical English. Similar correct sentences would be "She's in the back of the hall" or "She's back in the hall" (note that these have different meanings). As you point out, it looks like the speaker was trying to use back as a preposition, but it can only be used as an adverb or noun.

I finally got a satisfactory answer from an episode of "A Way with Words". In short, this appears a case of locative prepositional deletion where "back" is still functioning as an adverb but the preposition (which could be, e.g., "in", "down", or "through") is omitted. Like the instance AWWW discussed, this appears to be a regional variant located in and around the great state of Pennsylvania (see updated details in the question).

While I would agree that this is not correct English I would question the way in which it was said. The origin of the speaker may well have influenced what was said. By adding an apostrophe it becomes "She's back 'the hall" suggesting either "in" of "of" have been omitted which would be perfectly acceptable for someone from, for example, the Yorkshire region of England.