What you could do is set up the projector and project on the side wall by the door (photo 1). Just use the wall as the screen. Mount the projector on the ceiling (3 screws) and one screw to hold the cords, or put an inexpensive wire "book case" and use the top shelf for the projector (inverted - upside down).
While I don't have a rental, I kept mine temporary since we are getting the heck out of the DC area in two years. All wires run along the wall and I can have everything down and patched/painted in a few hours. Since it is in the basement, it only has to be functional and not for show.
Pictures: projector/mount, wall/screen, Walmart light blocking curtains over the upper window and sliding glass door (door also has vertical blinds), and a cheap Amazon Garland "town center" ploy (ie. light weight) rug on the side.
I put up the rug and it does a great job of reducing reflected light. Unfortunately I nailed it up, but while covering other areas with a second rug, I found it is easier to cut a rug in strips and use blu-tac to secure it to the wall. At $39 a rug, it would make a great border for a screen by cutting it into sections. A $79 dark 7x10 indoor outdoor rug covers the off-white carpet under the screen to reduce reflected light.