Unfortunately, I don't have time to work on this today -- I'm about to leave for an astronomy trip, so there's all the packing and stuff. If I do have time to work on it during the day over the next few days, I will. But if someone else wants to look into it sooner than I can, please do so.
Workaround: Avoid altaz grid and horizontal coordinates.
Some developer information: While I believe that the transition to CachingDms could be responsible for this, I haven't found any immediate evidence. The problem seems to be:
1. A line that returns a Vector2f(0, 0) in Projector::toScreenVec instead of failing an assert and crashing (added in Android transition efforts)
2. A call to NoPrecessIndex::JITUpdate() seems to mangle the azimuth. I guess this is the effect of calling HorizontalToEquatorial and then EquatorialToHorizontal when altitude = 90.0 (i.e. when alt = 90, azimuth is indeterminate).
3. It should be okay to set the azimuth to something finite just so computations don't turn out to become NaN all the time -- but I would refrain from doing it in toScreenVec, since it is called a million times per draw under certain settings.