Righty so I love distortion, it's my number one favourite effect. Right now I have a vintage big muff clone and I loves it to bits. Shame it's not tight or smooth. Also have a MI audio crunch box, which I'm looking to replace, as I don't want that mid humped tone that the CB does so well.
Lol, the CB is anything but mid humped. It's quite a mid-scooped pedal really.
But then I listen to your link for the type of tone you're looking for, and it appears you really want NO mids whatsoever.
You'll need something with a mids control that you can turn to zero.
I'd be surprised if you couldn't find one of the Blackstar pedals that did exactly what you want. They're pretty widely available now, try and get to audition them withh your amp somewhere.
HtH suggested getting an EQ pedal, which I think is also a good idea, and may help you transform your CB into the tone of your liking. A load of very mid-scooped players are fairly dependant on EQ pedals for their sound.
Sounds to me like you're maybe not greatly experienced at playing loud in a band setting (please forgive me if I'm wrong). Be very aware that when you cut out too many mids, you will be utterly lost in the real life situation of a band.