poscaenium ~ poscēnium is the name for the place behind the wall of the stage, and is probably what you're looking for, e.g. in poscēniō. It's derived from the phrase post scaenam ~ scēnam "behind the stage". The Roman theatre only had curtains in front of the stage that were lowered to reveal it, so the service space that for us is behind the ...
Latin certainly allows “stand-alone prepositional phrases,” and I'm sure you already know a few of them, for example:
ante meridiem, post meridiem (a.m. / p.m.)
ad hoc, ad libitum, ad inifinitum, ad nauseam
in absentia, in medias res, in memoriam
de iure, de facto
ex cathedra, ex post facto
So I see no problem with ultra aulaeum, for example.