Supination is required to get the most out of your biceps! Forget about the EZ bar!
Also throw out Hammer curls! YES i know hammers are a great overall arm developer, but save it for training forearms, when you combine it with reverse barbell and reverse cable curls!!! Instead use the oppertunityh to replice it with yet another supinaating exercise like concentration curls!
Splints.... if barbell curls are hard on your wrist Start with dumbell curls and do scott curls after that. Scotts force you to go somewhat lighter on the weight, but the intensity will be there and when you finally make it to the cheating barbell curls you biceps will be exhausted enough and wrist will be warmed up enough so that the lighter barbell curls will not hurt your wrist!