OK, your price range looks reasonable.
It's possible to make a 2D position sensor based on one or two scanning lasers. Normally, these are very expensive devices, but keith1024 has been modifying SF02/F lasers to do area mapping Laser Measurement (SF02) Setup & Library - Sensors - Arduino Forum
It may be possible to place these in the back corners of the stage to provide a 2D map of anything on the stage area. I think that keith1024 is going to provide mapping software for the Arduino so I'm sure you could ask him to modify it for your application.