After a fair amount of trial and error, I have finally discovered a way to back up files on one system over the Internet, to a remote system in a secure, automated way.
Included below are some commands that I have found, created or tweaked to help make life easier along the way. I have collected them here so I can easily refer to them instead of buildling up the commands from scratch. Some are very simple, others are approaching "script" level. Hopefully others will find them useful as well.
Find and compress all PNG files under the apache web root:
It's actually surprisingly easy. Install fswebcam (preferably via RPM) and then run this command:
/usr/bin/fswebcam --quiet --background --loop 120 --skip 40 \
--timestamp "%d-%m-%Y %H:%M:%S (%Z)" --png --palette png \
--font /usr/share/fonts/liberation/LiberationMono-Regular.ttf \
--resolution 640x480 --info "Web Cam Stream" --top-banner \ --save /var/www/webcam/webcam.png