Tree billboards clipping into terrain

Hello lovely people,

I am playing around with terrain generation, and I am having trouble with tree billboards clipping into terrain when viewed at a high angle (as pictured below). I believe the problem is that the tree billboards are anchored at the base of the tree, and the slope of the terrain means that the terrain "cuts off" the top of the trees.

I would like to have quite a lot of trees view-able from this distance at this angle - so increasing the billboard distance is not an option for performance reasons. Any options I am overlooking? Perhaps there is a way to lock the billboard's rotation in such a way that it will not clip into the terrain?

If you have experienced this problem before, please let me know what you did to work around it! I am stumped.