I'd avoid the extract and puree altogether. I might add puree to the whirlpool, but probably not.
I find I get good peach flavor by macerating the peaches and adding them to the fermenter. If you're using a conical, after you dump yeast the peach chunks tend to act like a filter. They also block your racking arm, so you have to do your transfer from the bottom of the cone.
Adding them to the bright should also work, but I find that carbonating on top of the peach pomace makes a different set of problems. The peach mass floats and makes a mess of your sight tube, PRV, etc. Maybe if you had a huge stainless tea ball...?
One other thing...peaches have a lot of pectin. I use a little pectic enzyme to eliminate that part of the equation.
Good luck! Send me a bottle!