RE: But what about offhand...
Practice good shooting dicipline listed abover and practice, practice, practice. I practice every day, mostly offhand, at 20,30 and 40 (occasionally 50 yards just for kicks) I plan to use a rest since all my stands have them. But, that way I know that I can shoot no matter what the situation presents.
But the biggest factor to improving shooting is a bow with a good trigger. Should break at no more than 3 lbs and minimum creep. Believe it or not flinching may be causing your flyers. And a poor trigger just increases the likelyhood of a flinch. We know the x bow won't buck but it's only human nature to tense up at the shot. Watch for it, then go back to good shooting dicipline.