I quite like the dual-use card idea. It's a little complicated, so it could be introduced a little later (but not too much later), as a ring-slot or something. I feel like it more differentiates the classes from a base level, as well as helping to solve the "I can't do anything so I'll just run this turn" problem. Granted, the classes are already distinct, and it might not be needed, but it's a neat idea!
Another possibility is to allow you to "tap" or "activate" an item in each battle that puts a card directly into your hand. This would allow for further power balancing among items, and could maybe require a cost of some sort ('activate' your wand, discard a card, gain a Zap). You could either limit the use to once per battle, once per item per battle, or limit it per character (X activations per battle). And yes, the added complexity is not necessarily a positive, just brainstorming here.
As long as the tapable item is limited in power, so we don't get people getting guaranteed 10+ damage cards every turn. However, there ARE cards out there that draws specific cards out there, so with the right deckbuild you'll limit your lack of certain cards.