4.5mm?! That is going to mess your hand up like DB said, it will lead to tendonitis or RSI. If a low action hurts your hand, it sounds like you might be holding the bass at an unusual angle. Try adjusting your strap so the bass sits higher and then shim and get that action down, then work on loosening the death grip on the neck.

Personally, I find 2.5mm at the 12th a touch high even. A lower action should mean easier playing if anything.