Yeah I'm like Heavier Than Hell aswell - highish setup and 11 gauge strings (Actually thinking about moving up to 12's cos the ones I've got on now are starting to feel a bit slinky, and yes I tune to standard)
I actually find it nicer to play rather than have the strings flopping about all over the place and its good to dig into, but everyones different so get it done how your like.
It does tend to sound a bit "woodier" if its higher up aswell (which is a good thing) but if the preamp gain is cranked hard enough it probably isn't that noticable. Clean tone is definitely affected though and it certainly shows.
Agree with Twinfan new strings will make a lot of difference aswell.