To be honest, I'm not overly interested in black skies and white trees -- it's a very overdone theme in IR. And it doesn't always work -- the dust filled air of SE Asia meant most of my IR shots didn't amount to much (no black skies or specular highlights) the way it does it clearer locales. Personally, I like to shoot IR because of the way it renders highlights and brings out details in things like old wood. Stone, like you, I wouldn't waste any precious HIE on the moon or sun, but it's worth thinking outside the box and trying new things. I appreciate that others may have tried it before, and that's useful to consider, but I'd like to see images to judge for myself.
In any event, in some of my research, there was reference to how even the dark parts of the moon may reflect IR, so it might be interesting to see what it does with a half moon (unfortunately we've had a lot of rainy/cloudy days and nights recently, or I'd try it myself).