A/C escaping down the staircase
When renting a victorian back in the day we did the same thing, we draped a sheet over the stair case to trap the cold air above. So...I think your curtain idea is perfect. Shouldn't be that hard to install, isn't permanent, but should be plenty to block the cold air from escaping. 

A more permanent enhancement to that system would be to place a ceiling fan upstairs to help move the air around even more. For now, a floor fan may be enough to help.