Cross-Level communication for streaming purposes


I’m trying to get (randomly chosen) streamed levels to align with each other. I’ve gotten so far as streaming a level (and even multiple instances of a level) with an offset but my next step is to determine a ‘correct’ offset for the subsequent streamed level, based on the orientation (and position) of the previous one.

Consider this image as something I’m working towards:

…and the ‘blank-4’ domino is my first sub-level. Now consider that the door to the next level could be on any of the three sides of the ‘four’. In order to provide a correct level transform for the subsequent level (four-three), I need my sub-level (blank-four) to return information about the chosen door.

Does anybody have an idea how I could go about doing this?