Tar,
I can tell you for a fact that if you order a balanced prop from some of the well known prop guys, you may get one that balances as you describe. In other words, some consider this to be balanced. I must say that I disagree with this though, but I have run said props without issues, so it really depends on how perfect you want it. In my opinion if the prop is perfectly balanced, it will always stop at a random position on the balancer...not repetitively in the same position.
What you are describing is a prop that is evenly 'heavy' on both sides of the HUB. In other words, as it sits on the balancer, with both blades level, one blade has the trailing edge down, and the other has the leading edge down. These are the areas you have to work on to eliminate the unbalanced condition. Mark both areas with a marker and file the corresponding leading and trailing edges until it balances. You should also pay attention to the hub itself and make sure the extra material causing the imbalance isn't there also. I have had some that actually required some material removal on the heavy side of the hub in addition to the blades. Also if the hub isn't drilled on center sometimes you can never seem to get a particular prop to balance properly no matter what you do. In this case, get another prop or accept that it balances horizontally and run it. If you notice premature strut bearing wear, you know where it's coming from!
Hope this helps a little.