Partially dead digitizer - any way to change slide to unlock?
As pointed out in my comment on the question itself, you might try a lock screen replacement from Google Play that might let you customize where to place the "unlocker". Just picking some examples by their screenshots:

  
LockMenu / Zipper Lock screen / WidgetLocker (click images for larger variants)

As you can see, there are multiple solutions available letting you define where the slider (or whatever) should be located – so you should be able to leave out the "dead spots" easily.