Or Squeezer on android will control a Picoreplayer install with LMS. I think you could try a USB connection to the dac rather than go the digi hat route as well.
Surely the NAS has some playback software, and you could stream directly via USB to the DAC? The Synology has Audio Station, I think I’d try that first before getting extra stuff, it might be fine.
If you got a Pi then you could install the picoreplayer, and use the NAS as server. The pi would be plugged into the DAC via USB, so the NAS could be away from the listening room.
Btw that DAC isn’t the one I have; mine are the Sanskrit Mk2. They are slightly more expensive than that, although all DACs sound the same.
I’ve got all manner of Google chromeand Amazon stick Sonos things here but none of them will pass DSD on, app I’m using on my phone is BubbleUPnP which is a breeze.