I'd be surprised if lime did much better than plywood. At least the American varieties of Basswood are very, very soft. The real appeal of the stuff is that it is fairly light and does not tend to break along the grain , so you really do have to cut it. But plywood doesn't split particularly readily either - even the cheap crap - and is probably made out of a harder wood. It's difficult to find stuff significantly softer than Basswood.

What probably would make more of a difference is really fixing the covering down onto the wood. I suspect the sort of leather used also makes a lot of difference. Rawhide for instance can be very hard; to the point of being brittle, so long as you keep it dry.