I think I have a solution for the aluminum slipperiness problem. Violin rosin! I'm going to get some and try rubbing a bit on the end of the ocarina. That should increase the friction on the surface, since that's why violinists use it on their bows. Furthermore, it can easily be removed with a bit of alcohol, so there's no permanent damage to the instrument. I don't think it will be visible, either.
Ubizmo
How about beeswax?