Question about DSD DACs

Apologies if this has been asked before (it probably has), but I'm a little confused about how DSD is decoded in the newer DSD capable DACs. My current disc spinner is a Cambridge Audio 751BD universal player which, according to the owner's manual, can output native DSD only through its HDMI output. Since my DAC (Bryston BDA1) has no HDMI input, playing SACDs can only be done through an analog (RCA) connection to my integrated. With this connection, as I understand it, the signal is output as PCM, though what its resolution is I can't quite tell. What I CAN tell is that the resulting sound is rather shrill.

At some point I'm thinking that I'll want to upgrade my DAC to a DSD capable one, but I'm not sure how these newer DACs process SACDs. Will I hear the signal decoded as DSD without conversion to PCM? Some DACs (like the PS Audio PWD MK II or Bryston's BDA3) boast HDMI inputs but I couldn't tell from their literature whether it's even possible to use this connection to a disc spinner to play SACDs in 2-channel, or how the signal is processed through such a connection.

Thanks for your help with this--it will assist greatly in making choices when I decide to do this upgrade.