Is it possible to purchase a replacement remote (SKU: 3226000173), or another that's compatible with Roku 3?
It appears that the headphone jack is failing: Moving the headphone plug causes audio dropouts. (I did try with other headphones, same result.)
Failing that, what is the least complex upgrade for the Roku 3? I don't need voice search or any of the other fancy features on the newer models. What I do need are a wired Ethernet input, an HDMI output, and a headphone jack on the remote.