I have a similar issue in my band. My guitar player uses a heavy Les Paul though a Bogner amp with a Bogner 4x12 cabinet, the combination of which generates a ton of low end bloom; especially on hollow stages. Even though he cuts the lows on his amp to 9 o'clock, he is still rumbly and blurs up my sonic space to the point where everyone is looking at me when there is boom on stage, even though I'm not playing. Even worse, we have a keyboard player that uses a full blown 1000W PA system as a personal monitor. His generates a ton of low end with his left hand. As a result, I get totally lost in the mix. It got to the point that my sound engineer begged me to play with a pick, so that he could slot me better into the mix. That actually solved most of the problem, and I really do enjoy playing with a pick, so I did that for a while, but then figured there had to be a better way.
I did a lot of research and experimentation, and recently I found an excellent solution. I was playing my basses (with Precision pickups) though either a Markbass 2x10 combo or an Alembic F1-X and an Epifani T410UL cabinet, depending on the size of the room. Both rigs are excellent and sound great, but are voiced to have a noticeable, and very satisfying bump in the deep low mids. Consequently, they sound muscular, but they can rumble a bit on on a hollow stage, and that boominess and rumble is aggravated by my low-mid greedy guitar player and the left hand of my keyboard player. Everything was a blurry mess. My solution was to go with a tighter, more precise amp (Glockenklang) which helped quite bit, but didn't fully solve the problem. The silver bullet was when I switched to a more neutral-sounding cabinet that didn't have a pronounced, built in low-mid hump, a fEARful 15/6/1, (the OP's MI112 cabinet is also excellent in this regard). I gave the cabinet a little bump at 300-350Hz, while cutting 2k by 3db. Voila, problem totally solved. The difference on stage was profound. My sound engineer could not believe it. He was delighted. Not that I ever need to, but if I want to I can get crazy loud with no boom, and I mean no boom whatsoever. This new setup is fantastic. Best of all, everyone on stage can hear me. With the addition of that 6" speaker in my cabinet, my on-stage sound dispersion is excellent. Now, whenever there is boom onstage, everyone looks at the guitar player. PERFECT!
I bet most of your problems can be solved with EQing, and am curious to learn what happened when you bumped 100Hz and 400Hz, like Duke suggested. If that doesn't work, and you haven't tried playing with a pick, please do give it a try.