Usually "musical" means enjoying the music as a whole but can also be at the expense of detail and accuracy. What you are looking for is an "articulate" subwoofer where the bottom notes sound like real instruments and not a boomy mess. Finding an "affordable" one seems difficult - I’m in the same boat.
Maybe Vandersteen 2Wq or Sub3 may fit your needs. There's also the AudioKinesis Swarm, but I'm not sure how articulate they are. Other articulate subwoofers are priced higher : REL, NSMT. Funk, Perlisten, JL Audio...
Good luck