I ran tubes back in the street stock days (could not use beadlocks) and cut them constantly. I would make sure that the wheel and inside of the tire were clean, cover the tube in a ton of baby powder, and still had problems. With the low PSI, it usually was an issue with the tube rubbing against the tire, a little bit of debris rubbing the tube, or the tire twisting on the rim (even just a little bit) and would cut the valve stem. I was able to go a little lower on air pressure, but had some serious issue with reliability. Maybe there is a racing tube that is stronger than the stock ones I used.
With the screw idea, it would help keep the tire from twisting, but not sure that it would help keep it from pulling off of the rim in the turn.
I'd love to see right rear beadlocks become legal.