The following is a model I built based on the ideas I ultimately came up with for the four units. From stage left to stage right, the dispatch would work by flipping around vertically, Abuela's apartment would slide out with a pair of walls which would fold open, the bodega would spin in place, and the front wall of the salon would fold open and allow the interior to slide out. The dispatch also had a platform that slid out in the same way that the salon platform slid out. This is not shown in the model.
The salon opens.
Stage right was trickier. The mechanisms for opening the two facades were both more complicated, and they were complicated further because they overlapped each other backstage when they both were in the closed position.
Unfortunately, I no longer have the scale drawings, but these illustrations serve sufficiently. As it shows, the upstage left corner of the dispatch platform is cut off by the stage right corner of Abuela's apartment.
To fold the swinging wall to the open and closed positions from backstage, there are two ropes, indicated by the dashed teal lines, which can each be pulled to operate the wall. One of the ropes simply runs backstage and is pulled to open the wall. The other rope is ran to a pulley inside of the fixed wall, and then it runs through the wall to backstage. This rope is pulled to close the wall. Both ropes run discreetly along the floor of Abuela's apartment.
The dispatch was the tricky one. There were two main problems. First, when the 19 foot tall wall spins, it would hit the stage right corner of Abuela's apartment backstage. Second, the act of spinning this wall created a gaping hole in the set through which the audience would be able to see directly backstage.
To solve this pair of problems, I needed to figure out how to achieve a sort of "spinning space" for the dispatch wall. This would be a completely empty space backstage at least ten feet deep and with the width of the wall in which the wall could spin. It would need to be covered on all sides in black to prevent the audience's sight from reaching farther backstage.
To allow the removable corner of Abuela's apartment to bear the weight required, I made notches in Abuela's platform's frame which the corner piece connected into. This allowed weight on the hypotenuse edge of the corner piece to be transferred to Abuela's platform, while the other two sides were supported by the stairs themselves, and vertical beams that extended down to Abuela's lower platform. This is highlighted in the image above on the right.
The dispatch platform, which had on it the dispatch desk, was pushed out and pulled in from its upstage side by an operator with a long pushing stick that was attached to the platform. The length of the pushing stick helped the operator to not be seen by the audience.
I also kept a stash of emergency supplies, including drills, screws of all sorts, flash lights, gaff tape, and staplers. It was a nice cozy cave.