Remember that when you're setting a high limit this is also when the cable tension is ramped up; i.e. you should push the shift lever to apply tension while you set it, because quite often once you've set the limit screws you then need to dial a bit more tension in to the cable with the barrel adjuster(s). When the cable is not fully tensioned the mech might not move all the way to the limit point on its own.
Remember that when you're setting a high limit this is also when the cable tension is ramped up; i.e. you should push the shift lever to apply tension while you set it, because quite often once you've set the limit screws you then need to dial a bit more tension in to the cable with the barrel adjuster(s). When the cable is not fully tensioned the mech might not move all the way to the limit point on its own.