The strap that goes around the base of the cheek bone needs to be tight too. I often do the nose and cheek strap up and then do up the headpiece another hole.
yeah nose part is twisting throat lash is on tightest hole.
would lunge in bridle but have a martingale and would be a pain to keep taking off putting on again to ride next day.
Can you get any more holes put in the straps? It just sounds as if you're not able to do it up quite tight enouogh.
Please don't lunge in a bridle - it causes so many resistances, the bit action is altered and all you achieve is to exercise your horse. You cannot work it correctly off a bridle with a single lunge line.