I'm on my 6th gen as a shielder and I still have this problem. I've determined it's related to positioning; good 2h-ers always try to stay just off your right shoulder. That's the "dead zone" for 1h; there is nothing you can do to someone there. If you left swing, it takes forever to get there and will probably glance when it does. Right swing will definitely glance, overhead used to be an option (albeit a risky one) before the turn speed change, now that's generally suicide also. Thrust is also out once you are in facehug range (the preferred domain for 2h; go figure).
2h has no such "dead zone", but you should at least battle to keep them positioned off your left shoulder, which is the only location from which you can hiltlash as a 1h-er. You can also sometimes execute a right swing against someone on your left shoulder if you turn left fast enough during the swing, but generally right swing is a bad idea against anyone that is aware of you (too slow and prone to glancing).
In general, if you find yourself turning right for most of the fight as a 1h-er, you are probably screwed. If you are turning left, you are probably positioned correctly to use your one good swing animation. I try to find obstacles (walls on siege, for instance) that I can hug with my right side to keep people from getting in my dead zone. Must be nice to be 2h and being equally deadly from any position!