Right, this might be a really stupid question but can you lunge off a dr cooks by taking the reins off and clipping the lunge line to the rings where the reins attach?
You'd be replacing the rein pressure with the lunge line and pull the horse's nose into you. the whole thing would close up on his muzzle. Without the bit I can't see how you could possibly structure an overhead check to off set this. Try lunging in a lunge cavesson headcollar - far safer!