or… sell the decklink and get a MXO2. then you can take it mobile with a laptop to record from the camera when practical, as well as use it when editing. it has color managmenet on the HDMI port specifically to work better with LCD monitors.
however, your decklink _should_ be playing back. the reason it isn’t is that your video out setting doesn’t match your TL settings. both have to match. yet another thing that desperatly needs to be fixed in FCP – that FCP can tell hardware what setting it should use directly and just do it.