For a lot of his fills that apparently make everyone in awe, all I hear is really fast rolls. And I say this as a drummer.
I think most of us who like his drumming is in awe not of his fills. His strength is in orchestration. If one looks for fills, Mangini is not the man.
And his orchestration, with some very very great exceptions, is doubling other people. You seem to love that. That's cool. As I said, to me it's more of a novelty that he is overusing. You've stated you don't want the drums to stand out or be "flashy" and I do at times. Just different tastes.
Sometimes his doubling thing works insanely well. Like in OTBOA when he's playing the guitar and keyboard parts at the same time. But eventually it becomes monotonous because the rest of the band are often doing the same thing. So instead of multiple things going on and being interesting, you just get everyone doing the same thing and Mangini really hammering it in. Just not interesting to me.