OK, here is a guess - You state you are using a "lead free" bullet. Typically, lead free bullets are longer then lead core bullets of the same weight. Longer bullets, for caliber, require faster rifling twists to stabilize. I don't know the twist rate of your barrel, but I'd bet it's too slow for the bullet you are using. Try a 32 - 34 grain bullet with a lead core, and see if that doesn't stop the tumbling issue.
Larry