Get a new set of dies, it sounds like there is something wrong with them.Ah, like a handgun. Nope. Getting it started isn't the problem, the die making it worse is. I see what you're saying but the die has enough play in it for the toe of the bullet to be bulging off on one side hard. I even had one that was fairly straight, but it had egg-shaped the neck, just off to the side like a bayonet.
I have several Lee die sets and have not had a problem with any so far.