Charlie,
So sorry to hear about your mishap. Better get that knife sharpened.
I have fashioned a tiller of oak, which I plan to use at first, and make a new laminated one of ash and makore or mahogany as a winter project. It seems to me that a laminated tiller would be much stronger than solid wood, but maybe I'm wrong. Perhaps the weakness was in the plywood layers since half the grains run laterally, but that's just a guess.
I hope the oak tiller holds up, given that it is only 3/4" thick. That's one thing that has bothered me about the rudder, the tiller slot is so narrow that the tiller has to be very thin. It could be made thicker, but you would still have to narrow it at the slot end, so what would be the point? Anyway, if the oak tiller does hold up my plan now is to store it in the boat as an emergency spare, when and if I get the new one made. You can purchase them custom-made. Pretty expensive but might be worth it, given my woodworking "skill."