Beyond Compare can't "open with" Notepad++ for remote files, only for local files because BC sends the full remote path to the "open with" program. It's on the BC wishlist but simply not yet possible.
BC does not use local temp copies of remote files the way WinSCP does. Also, NPP itself can't open remote files because it only understands local files (it has no SFTP interface).
So there's currently no way to do what I want to do. Stick with WinSCP, or stick with BC, or use a mix depending on what's important in the specific task.