BricxCC not seeing Serial Tower in Windows 10
A bit more fumbling around led me to an actual installer:
http://bricxcc.sourceforge.net/test_releases

I was hesitant to use that because of the word "test", but in fact that's what's needed to work at all.  Download bricxcc_setup_33810_20130220.exe from there and run it, and it "just works".



The situation above came from a zipped archive, not the installer.  Having rejected the "test" version, I then found the archive, unzipped it, and tried to use it.  Apparently, it was missing something that the installer includes.  Comparing the installed program directory to the unzipped one definitely confirms this!