I wanted to offer an update to my old post for reference purposes.
I did end up swapping my Roku Streaming Stick 4K for an Express 4K+ so that it would work with a replacement RF learning remote. I invested all of $10 in this one:
Amazon.com: Programmed All in One Remote for Roku Box and Vizio TV with Extra 9 Learning Keys to Con...
It's a pretty decent little remote. It came preprogrammed for the usual Roku functions. I programmed it to handle AVR volume (using the Channel +/- buttons, because they're easier to access than the dumb little ones on the side) and also to control Power for both the TV set and for the AVR. I also used the two "spare" function buttons for switching inputs on the AVR.
