If your cable box has DVI . . .
Then it must have a digital coax or optical audio output. Using this type of connection from the cable box and DVD player will allow you to receive a multichannel Dolby or DTS signal. The red/white RCAs are only a stereo signal.
Also, if you don't see a major picture quality difference between HDMI, DVI, and component, then take advantage of your receiver's component switching feature to minimize the number of video cables to the projector.