a cheap (and landlord friendly) way to stick a large plastic sheet on a wet wall?
If you have sufficient space, and in this case, it's not all that much, you could consider a modified lean-to for your purpose. A horizontal pole from which the plastic is suspended with a vertical pole at each end. The vertical poles would be vertical referenced to the horizontal sheet suspension pole, but not-vertical referenced to local gravity. Orbital dynamics are not considered in this example.

The poles would be longer than the distance from ceiling to floor and would not have to have much of an angle to keep the horizontal pole against the wall. The bottoms of each pole should be braced or have a rubber/high-friction end to keep them from sliding out. If the span is severe, it may be necessary but possibly undesirable to have a center support as well.