I want screen saver on and iTunes playing

I want to play music through my stereo while I am showing my house. I set up my iTunes on my computer, turned off the energy savers, set up my screen saver to require a password, and moved my mouse to the corner to start the screen saver.

After a while, iTunes stops. I got caffeine and tried it (set indefinate).

How can I keep iTunes playing, but have my computer secure while I am away from the house?