One way to make the best of what sounds like a bad situation: turn down the bass control on the amp. Or, as a previous poster said, set the EQ sliders in a frowny face.
The low frequencies soak up most of the amp's power. With more power on tap from cutting the lows, the mids will project better and the amp will sound much louder. Maybe add a little distortion. It's fun having bowel-churning lows, but its unnecessary.
Especially if you play venues with a massive sound system and an FOH engineer, who's going to roll your signal off below 80 Hz or thereabouts anyway.
(BTW, I recently read an early '70's interview with Felix Pappalardi of Mountain, who said that he always had the bass control turned all the way down on his Sunn stacks. Might have got the idea from Jack Bruce, who used only the bridge pickup on his Gibson EB-3.)
Here's a perfect example: what Danny Sapko calls "the heaviest BEHS tone I've ever heard." Sounds massive, but notice that there's literally nothing below about 100 Hz there. All mid-range and distortion.
But he recreates it by cranking the bass and turning down the treble and mids? I'll have to play around with the EQ a little, but I've really enjoyed a heavily scooped sound on my Ibanez (tuned to Drop A). For my Gretsch which I just keep in E standard I do like having a lot of mids present, but I'm going for a totally different sound with that one