Just an update - I went ahead and jumped off the cliff and started the project using 3DTin. My students are modeling the soccer goals we will be building out of PVC next week.
I had three students get the same problem as I had here. It manifests as a "white screen of death" - the whole screen goes white and pushing the various camera buttons does nothing. There seems to be no way to fix the camera values once it has happened. It definitely happens while moving around and zooming in and out (probably in orthographic mode, since that works best for our needs), but there has been no clear method of recreating it.
I have instructed the students that if it happens to refresh WITHOUT saving and to NOT recover their unsaved work. This sends them back to their last saved version which was, hopefully, soon before the white screen of death. So far, that seems an acceptable workaround, but it is obviously not ideal.
I find it surprising that this bug hasn't come up more often, since it has managed to come up four times in a three hour period doing very simple things, with different people, in my presence. Even if the bug cannot be locked down, I think some more graceful way of recovering from it should be implemented - if it has to do with invalid camera values, isn't there some way to force them back to something valid? Obviously, there may be more going on here than I understand, but it seems like this might be an important one to solve. I am contemplating purchasing a premium account for myself, and possibly looking into getting some sort of educational license for use at my school, but if this bug remains such a showstopper I don't really feel comfortable doing that.
I had another odd issue come up with a student too, which I will post about in another thread as it is not related to this one.