Thanks for the suggestion, @americanaudiophile. I want to make sure I follow:
I plug the Roku into an HDMI input selector then run an analog audio cable from the input selector to my amp. Then I'd fix a bluetooth transmitter to the HDMI out port on the input selector and pair it to a receiver...
I have an Optoma HD143x projector and a Peachtree Nova 150 integrated amp with a Peachtree BT1 bluetooth receiver.
My plan is to stream video from a Roku into the projector's HDMI port; connect a bluetooth transmitter (TBD) to the projector's audio out jack; and stream audio to the receiver...