The problem with Star dies, aside from needing interior polishing, is that the sizing occurs before the lube is applied. The bullet is being sized dry. I solved the problem by simply running a previously lubed bullet through, followed by about five unlubed ones, then another lubed one.
Veral Smith, on his page, suggests dissolving a bit of Lee Case Sizing Lube in some water, using just enough lube to make the water cloudy. Dip the unsized bullets in this, allow them to dry, and size them. He says it solves the problem. I haven't used this technique yet but I will the next time I cast any bullets.