Using a Roku with a digital-to-audio converter

Our TV is actually a large  monitor connected to an analog pre-amp, which is connected by RCA to speakers. Right now we have an Amazon streaming stick, which connects via bluetooth to a digital to audio converter.

We bought a Roku streaming stick this weekend, not even thinking it would not be able to do the same thing, and, sadly, had to return it as it won't work with our set-up. 

Before we go buying and trying things, I thought I'd ask here for some advice. I'm seeing that the new Streaming Stick Plus has bluetooth headphone capabilities... will that work? If not, will the Ultra Rokus work, or will they only work with other Roku devices?