Pair with a blue tooth headset like my Plantronics M70. Seems pretty straight forward since the remote is almost already that, except for the form factor. Speaking of form factor, how about a Star Trek style comm badge?
Pair with blue tooth speakers. Alexa sounds pretty good, for a 2.5 inch speaker , but i'd really have to crank her up in order to hear music in my bed room.
Have Alexa trigger a series of events, such as turning on lights, then playing music, or reading the news and weather when i say 'Alexa, I'm home.'
Use my name when i ask her to open the pod bay doors.
Optionally cut back on the commentary when I ask her to play a piece of music, I really don't need the name, opus, or key on the clasical stuff, an 'OK' would be fine. I can always ask 'what song is this', later.