I used to use the Tannoy concentric speakers in my music production lab back in the day. I remember they had an interesting signature that was not pretty but was good for digging detail out of a mix.
You mentioned the Soundlink Mini profile was sort of close. What would make it sound better? If you are able to get close with the bass and treble controls (let me know those settings) and give me a bit of artistic feedback (describe in colors, shapes, flavors whatever) I bet I can make a profile that works with your speakers.