The EVH's could work in a 4x12 with H30's. However, the H30's will be a lot louder than the EVH's so if you're going to do it, put the EVH's on top.
I don't agree that the pairing will be too bright though. I have two EVH 4x12 cabs and I don't consider those cabs overly bright at all. I've always thought of the EVH speakers as standard Greenbacks but without the papery high end. In other words, the EVH cabs have the midrange warmth of normal M magnet Greenbacks, but the EVH's highs are much smoother. They also might pair well with the H30's, which do have a spike in the highs as well as strong low end.
As for your question about the EVH speakers getting ratty with high gain, I don't think so at all. I have an EVH 100w EL34 and 100w Stealth, both of which as I'm sure you're aware put out a ton of upper harmonics and white noise with the gain up, and both of those amps sounds great through the EVH cabs.