So you are saying that in the dealer showroom you listened to your amp and a cd player that was the same model as yours, and they sounded much better. Given that, and given that usually the most significant determinants of overall sound quality and character are the speakers, the room, and the placement of the speakers in the room, it seems pretty clear to me that you should focus on speakers/room/placement.
I'll add that I still have a Rotel RCD-855, ca. 1992, which I suspect is not particularly dissimilar to your RCD-971, and it provides gorgeous sound with well engineered recordings (albeit through far more expensive electronics and speakers).
Regards,
-- Al