Sounds like it might be a cam timing issue. As mentioned, a slightly over or under rotated cam can cause some pretty funky nock travel and a darn near impossible to tune bow.

Not to insult your intelegence but just asking some of the basic questions.

1) when you measured tiller, did you use the bow string or a string stretched between the axles? Setting an even tiller with the bow string on a single cam bow will yield a bow that is significantly out of tune.

2) Did you change the rest to something like a prong rest to see if it would tune with that? I have never used the QAD rest, however I have had a couple of bows that simply did not like a particular rest. They would tune fine with just about anything else.