Sorry but ...a Mini PC with foobar2000, remote controlled via phone/web and a monitor for the full screen cover and done, that's what I'd do.
I think i'd just make the bezel for the display and putty an SBC onto the back with an HDMI converter dongle. I'd likely order a custom picture frame with some rococo moulding, for the anachronistic effect, and display nondescript oils when not streaming.