Does anyone have any suggestions? I include a reproducer below.

If the Popupmenu gets highlighted, that is an event you can piggyback on to change focus as well ... focus is found all over https://metacpan.org/source/MDXI/Curses-UI-0.9609/lib/Curses/UI/Popupmenu.pm :)

is Curses::UI hopelessly broken?

Ask yourself, is Curses::UI a cheesecake? :)