Lots of issues here. First, the ‘single prong output’ looks like a 3.5mm headphone style jack. At best, this would carry an analog stereo signal.

There is no RCA output on this projector, only an RCA input. Also, this projector has no ARC capability, in order to create a signal that could be read by the Sonos Arc. 

Essentially, the only convenient way to get audio to a Sonos Arc is to split out the audio before it reaches the projector. This requires an external device. There is the HD Fury Arcana, the Feintech VAX04101k, and the latest, is the OREI HDA-935. You can also order from those links from the companies directly, or check your local retailers for availability. Amazon may carry some, depending on location.

Alternately, if you don’t care about Atmos, and are interested in a cheaper solution, which provides Dolby Digital as its max output, you could go with most HDMI switches with an optical output, and connect that optical output to the adapter from Sonos, which would pass the signal to the Arc. 

Thank you for the prompt response to my question.  I never thought about a 3.5mm to optical converter, I only knew that there was a 3.5mm to HDMI converter available. I also never knew that the HD Fury Arcana would be a possibility for the soundbar after converting the 3.5mm output to HDMI.

Unfortunately, your response came too late...I just purchased a used analogue soundbar.  This solution is at least a start to some better audio from the projector.  

I will definitely keep your ideas in mind if I want to upgrade the soundbar.  Thanks again

Also for future reference, consider the Ponybro HDMI extractor. It is relatively inexpensive and I have found it works very well (i use it to split a signal and send Atmos to my non-HDCP 2.2 9 channel amp).

Brian