You can help minimize handshakes buy "fixing" the resolution of each devive to match the display's native capability.
If it is a 720p display, set the cable box to 720, the bluray to 720 and the 975 to 720p. The same goes if it is a 1080p display.
This will at least prevent the display from relocking to every signal change.
Do not leave anything on AUTO.

Try that and see if it helps.