What would MY band sound like?

I play with three different bands, a soul band, a jazz band and a guitar/voice, saxophone duo. They are all fun in their own ways, but seem to be run by someone else, so I don't really have much say in musical direction. This suits me in lots of ways because the bands are fairly successful as they are, so why change things. But I feel the need to have my own band, to dictate the way we play, to choose the name, to run the project from my own criteria and experience.
The soul band is purely a working band, doing gigs for money by providing entertainment. This fulfills my need to earn some bread and butter and is a lot of fun, playing classic soul songs.
The jazz band is more about expression and learning the art of jazz and swing. And we earn money.
The guitar/voice, saxophone duo is mostly for lively pub and club nights. We call ourselves The Vapes, because we're both vaping enthusiasts.
So what would MY band be called? To give some impression of what I want to play in MY band I suggest you listen to Australian minimalist impro band, The Necks.
I'm playing The Necks in another tab on You Tube as I write this, a 56 minute long track called "Sex". I'm in love with the sheer repetitive sustain of a simple double bass, piano and drums groove.
Trouble is I don't know any other musicians who have the courage and sensibility to sustain a groove at a minimalist level for anything more than a few bars. Everyone I work with is more concerned with entertaining the audience by ramming out 4 minute songs with AABA structure.
But I want to play music that is like "Sex" (The Necks track, not the procreative kind).
Maybe I shouldn't even attempt to find fellow musicians with such a rare creativity that they could sustain a simple groove for the length of a whole set? Maybe I should use my loop pedal and do it alone, but perhaps that would be more like "Masturbation" than "Sex"?

The Necks - "Sex". (1989)