Also a good idea
Few weeks back I forgot to pack my trusty DM screen, and was having difficulty using a loaner, so I cleared my end of the gaming table, set my adventure/map notebook on my lap, and rolled 'em for all to see. The lack of a physical barrier has made a noticeable difference in the game which is difficult to describe, but it seems more of a group effort, as opposed to an "us against that guy with the screen" dynamic. Anyhow, its back in my D&D bag, but now it lies flat on the table. I say, ditch the screen!
However, if you like your screen, here's a 10GP idea for ya: get some of those black spring-steel paper clips, and attach a few to the bottom when setting up. Bigger clips provide a broader base, and the added weight keeps it upright even under the impact of a wildly-flung d30. These will tend to mar the screen over time, but you could prob wrap them with duct tape to provide a cushion between the cardboard and the metal, or maybe sandwich the screen between two additional layers of cardboard before clipping.