Box/boxwood also suits, if you can get the stuff. Expensive, but very hard, and among the traditional woods for the purpose. FWIW, I would agree that the OPs hard maple is mislabeled soft maple.
Distinctly lighter rather than dead white is the rule for most woods - Holly is one of the few that is both somewhat hard and really white. Tagua might be an option, but tagua that large is not anything I'm aware of being out there. Even a pure white wood will not stay white if the set is actually used, of course.
Basswood is loved by carvers in part becasue it's very soft and light, easy to carve - so not at all what the OP is looking for.