I use and love evm12L's, and on top of that I'm currently making plans to drop them into my Gflex 2x12 oddly enough! I'll tell you what works for me since our tastes seem to be similar
I would lower the bass, or use the bass cut, or both. Then start to roll off anything above 4-5k if you pick 4k to start, be gentle, if you pick 5k you can be pretty severe but I would do this while the whole band is playing if at all possible. Here is the part that really sounds gnarly when you play alone tho, the 1k slider. Chris suggested this already, and I just have to back that up. I've really been learning the power of the 1khz slider lately, and it's been pretty amazing...
first of all, I think 1khz sounds like garbage on a distorted electric guitar, I just have to say it. It's fizz and spit and just about everything I hate in a guitar tone, so for years I've been dialing it out every time I dial in a tone on my own, and getting the same problems you are where I just don't cut. Now if you goose it up a bit while everyone else is playing, it will feel almost like a "cut" knob. One slight bump over "just enough" can be "omg way too much" but play with it a bit, it's worth it.
Also, keep in mind that if you find a frequency you like or hate, you can get an octave above by doubling it, or an octave down by cutting it in half. So if you find 1khz to be as important as I have, you might try messing with 500hz and 2khz. I often find that it doesn't mean you dime 500,1k, AND 2k just because you like 1k tho, but rather I might lower 500 very slightly if I go crazy with 1k, or that maybe I don't necessarily have to go so crazy with 1k if I lightly boost 2k as well. The doubling/halving "rule" just shows you other points of interest, doesn't mean you can boost/cut them all the same way.
Hope this helps!