I agree that if you want a fatter, warmer tone, you can get it picking more towards the neck. OTOH, when a twangy, biting tone is called for, picking closer to the bridge will get the job done.
I move my right hand around depending on the situation.
My Tele absolutely sings through the LSS. Both clean and gritty are spine-tingling.
I have played a PRS McCarty and a Gib ES-335 through it quite a bit as well, with pleasing results. However I guess I agree with the folks that say EL84's and single coils seem to go together.
I have a G&L ASAT...
All this talk of the "brown sound" and I still have no clue what that is. :D
Anyway, try the amp settings database:
http://www.grailtone.com/tone-settings/mesa-boogie/mesa-boogie-amp-settings.html
I bet the rectifier tube went. Mesa had some bad ones (mine went out too). When that happens, the 30w mode still works because the solid-state rectifier kicks in on that power setting.
You should definitely try out both Lonestars (Classic and Special). They sound quite different but share a lot of features (versitality, wonderful cleans, etc.).