The DeckLink Pro is a standard definition card. It will always down convert your HD clip to your SD on output. That is why the option to turn down conversion on is greyed out.
The Mac’s internal audio runs on a seperate clock from the card’s. This is why you’re getting sync issues. Please monitor audio off the DeckLink Extreme card instead and you should be fine.
Actually, I might be wrong. Turn on hardware down conversion and use the SDI B output to connect to you SD monitor. This way, you can monitor SD via SDI and HD via DVI.