muchpa' is fine for "theater" (or "theatre"), but a better translation might be "auditorium." Maltz agreed with your observation that it's kind of close to puchpa', but he said that, given his viewing of Terran plays and movies, that might be apt and it didn't bother him at all. If "Bloomsbury Theatre" refers to the whole building — auditorium, lobby, dressing rooms, puchpa'mey), not just the room where the performance takes place, he'd go with much qach.

(email to De'vID with words for the Festival of the Spoken Nerd)