Well I would just like to say I don't know if there are any coyotes in your area either, I was just taking a guess that there was. If you have a lot of reds in your area try a bird in distress, I have been having great luck calling in reds with yellow hammer woodpecker tape from Johnny Stewert. As far as your bow setup goes, I would stick with your big game setup, after all your already familiar with it. If your aleady shooting a release I would stick with that also, it sounds like you have a short axle to axle lenght on your bow, and that would be a big reason why your accuracy falls apart when trying to shoot with fingers.
Best Wishes and Good Hunting