Despite the fact that cPanel was showing an empty error log, a hosting tech was able to dig up the error. It fingered Wayfinder, which reminded me that there is a showstopping imcompatibility between WF and 2.1.1, requiring the former to be upgraded before the latter.
My inability to get into System Settings or Package Management was some kind of sessions issue, which I managed to solve by clearing cache, flushing permissions, flushing sessions, and clearing cookies.
So my site’s back to its old self now. Whew!
Jason