Thanks a million, djbob. While I didn't understand the 'mod_rewrite', I was able to googl it and find something that works. Basically my .htaccess file now looks like this:
AddType application/x-httpd-php .png
RewriteEngine On
RewriteRule .png /phpsigs/test.php
This allows ANY .png file to redirect to test.php, and that script renders the .png file correctly. Plus, with a little bit of trickery, I was even able to capture the image name, and use that inside the image.
e.g. http://beekay.heliohost.org/phpsigs/djbob.png will show a (very temporary) image withsome stuff and your name on it. There is no physical file called djbob.png, and changing the name to 'whowouldhavethoughtitwouldwork.png' will work too!
Thanks for all the help and nudges in the right direction.