How Would You Soundproof This Room?

No idea, but do you mean acoustically treat or soundproof, as the two are not the same?

Soundproofing is designed to keep the noise within the room and prevent it escaping or outside noise leaking in. Acoustically treating a room is largely about minimising sound aberations due to reflection and resonance.

Soundproofing would involve a lot more work and cost than adding acoustic panels to dampen down a 'live' room.
 
I would hope to achieve both at the same time.

Primary objective, however, would be to stop sound escaping, especially through the floor. Acoustic treatments could include rugs hung on the walls, acoustic wallpaper or other treatments to stop reflections, which is suspect will be the main problem for those wanting to hear the music.....
 

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