I'm running into the same issue with my Barefaced BB2's. There is no attenuator for the highs, just a crossover that redirects them to the speaker rather than the horn. So although it's not as bright and in your face sounding the high end is still there. Most of my dirt sounds are just meh to me right now, but it all started when I switched to Dingwall. With other basses and the same cabs it wasn't as much of an issue, but I like the Dingwalls to much to change them
I may look at different cabs but the BB2's are amazing so it's hard to think about moving away from them. I may try out their Two10 or Four10.
For the interm I recently grabbed a Beta DLX which is a much darker OD than my usual. It's been doing pretty well for me.