I could probably go into a lengthly discussion about how to time this thing right, but I'll give you better advice. Call Muzzy and ask to talk with Mark Land. He;s their ZE Guru. Or you might find him over on www.archerytalk.com
Your problem is not with the rest but how you have it timed or that you need to unscrew the turnbuckle a bit to get it to drop sooner. You should have it timed to raise to it's highest level about 1" to 2" before you reach full draw. Of course, maybe you have a low nocking point driving the nock end of the arrow down into the rest.
The moleskin on the hook is a good idea. It makes for a real quiet draw.