How do I fix incorrect attic insulation?
I have some in my attic (from a previous owner) and I've found that it's never the same after it's been disturbed.  All that "fluffing" will do is create an enormous amount of dust.

I think you need to install new insulation; you shouldn't need to remove the old insulation if you're adding more of the same type.  The new will just sit on top of the old insulation.  If you do decide to remove some of the old, a shop-vac works well; just be ready for lots of dust.

Personally, I prefer fiberglass batting because you can move it out of the way if you need to, and it will spring back if you compress it.  These days, you can get batts that are sheathed in plastic so that they are clean and easy to install: no fiberglass dust!  Again, they would just sit on top of the existing insulation.