I stripped the project back to just using an Activity (instead of AppCompatActivity) and now it’s complaining about android.support.design.widget.CoordinatorLayout being not found. There really seems to be something iffy going on with the support library (or libraries).
EDIT: I removed all references to support libraries and switched the CoordinatorLayout to a LinearLayout. Now it builds and runs fine.
EDIT 2: Found an old thread discussing a similar issue: