Two things might be happening here.
First, are you sure you have the back half of that hinge "hooked" into the back of the bottom plate? Depending on the hinge, it needs to clip under a set of fingers before you tighten down the front screw. Make sure when you are sliding them together you hold them as flush as possible, don't just rely on the front screw as an indicator of attachment (you will need to undue the front screw, pull them apart and when you reattach them, push them tightly together.
Second, If you are sure they are mated together properly, then you need to turn the depth screw (I believe this is the inner most screw on the long finger) counter clockwise as far as it will go until the screw either bottoms out or the CP sits flush.
Short of those two suggestions, the hinge might not offer any more adjustment as I don't think it was designed to sit in a final position as you are using it in your project. If all else fails, trace an outline of the small bracket that attaches to CP bottom and route out that area until the CP sits flush.
Let us know how you make out...