|laziness, impatience, and hubris|
That was the magic bullet. Thanks, Stefan!
Evidently I have a lazy text editor (however, it has support for DOS/Unix line endings, AND can do Unicode).
When I took 'test.pl' and saved it as 'test.pl' with Unix line endings, there was no difference. When I took 'test.pl' and saved it as 'testu.pl' with Unix line endings, it worked! Until I changed the name, it didn't feel like it needed to do any work converting line endings.
That solves the problem. All I have to do is convert over my template files to the correct endings, and I'm good to go.