One solution would be to go to Ground-Start trunks. A ground-start gives a more positive indication for answer supervision. Otherwise, you'll need to tweak the pseudo-answer timer that OBTW was talking about, and you may get angry guests.

Also, if you try it with a stopwatch, you'll find that it's tough to ring 4x and leave a message in less than 30 seconds.

Which SX-200 is this? Does it look more like a refrigerator, a bunch of matching PCs, or a microwave oven? What lightware?