Leaning doors

Good Morning Think Thank, I am needing some help, I am a high school theatre teacher and we are building moving door frames for our Fall Play. My students built all four and when we put them on their wheeled wagons, they are leaning, which causes the door to sag. How I get them to stand up flush? We building doors jambs (out of 2x4's) around slab doors. Do I need to build door frames around them now? Help Think Tank, you're my only hope!