I've got a Merkur. I drop the blade in and tighten. Never had a problem with uneven blade exposure nor had to monkey with it in any way. Gives great shave and words can't express how happy I am with it!
I have a Gillette Blue Tip which, like your parker, twists to open. Unlike my Red Tip (also a tto) the Blue Tip shifts the blade a bit to one side if I tighten down too hard on the knob. I'm pretty sure my blue tip isn't supposed to do this but once I realized I was torquing down too hard I simply didn't twist so hard and it became an excellent performer (albeit a bit too mild for my tastes).
Perhaps you could experiment a bit with how much pressure and how far you twist. Might just fix the problem.