Try pure nickel strings, D'Addario or Fender, in that order. That's the cheapest and easiest way to address harshness. Steel strings, even nickel coated ones, produce harsh treble, period. Pure nickel does not. Ask EVH!
Next, go to Michael's and get 20 oz. of polyfil and put it in your 2x12 cabinet. That will tame the harshness of the speaker's rear wave being reflected back through the cone. It will tighten the bass organically and produce a much more musical sound.
Past that, look at reflections in your room.
If your Mesa tubes are Russian or Chinese, consider getting JJ's. Nickel strings will likely make this a non-issue though. New production Russian and Chinese glass can exacerbate steel string harshness.
For power tubes, OG Russian military 6n14n's with NO SUFFIX like -EV or what have you are the finest EL84's for the money, and most durable. See Dr. Z and Tranwreck. They can be had cheap too.
Furthermore, if any of your guitars are using SD JB's in the bridge, they need to see 250K pots and about 125K total load to bleed off the proper amount of high end to ground. 250K total makes JB's and Screamin' Demons and the like super harsh in my experience.
I'd also rip out the cheap ass Marshall wiring and use some good thick wire in the cab too after the above was done just for added girth and enhanced speaker dampening. 10 gauge sounds more open, ask Reinhold Bogner!
Let us know how the experimenting goes!