Okay, I seem to have fixed this, but the repair is not for the faint of heart.
Somehow the WordPress Single File PHP Gallery plugin registered itself as active, but did not UNregister itself when it was removed from my system. So, it was stuck in the wp_options MySQL table. To get it out, I used phpMyAdmin and manually edited the entry.
Here is the process I followed:
1. Backed up my database!
2. Searched the table, wp_options, for the option_name "active_plugins".
3. The option_value for this option_name was an array of all the active plugins:
a:16:{i:0;s:19:"akismet/akismet.php";i:1;s:43:"broken-link-checker/broken-link-checker.php";i:2;s:33:"category-magic/category_magic.php";i:3;s:36:"contact-form-7/wp-contact-form-7.php";i:4;s:26:"dm-albums/wp-dm-albums.php";i:5;s:21:"exec-php/exec-php.php";i:6;s:43:"flexible-navigation/flexible-navigation.php";i:7;s:41:"gd-pages-navigator/gd-pages-navigator.php";i:8;s:29:"nextgen-gallery/nggallery.php";i:9;s:36:"random-image-widget/random_image.php";i:10;s:47:"really-simple-captcha/really-simple-captcha.php";i:11;s:39:"simple-ldap-login/Simple-LDAP-Login.php";i:12;s:49:"vipers-video-quicktags/vipers-video-quicktags.php";i:13;s:43:"wordpress-link-directory/link-directory.php";i:14;s:34:"wordpress-single-file-php-gallery/";i:15;s:29:"wp-recaptcha/wp-recaptcha.php";}
4. I guess that the first number (a:16) indicated the number of plugins in this array and noticed that the plugins counted from 0 to 15. That is, i:0 to i:15, for a total of 16 plugins. So, I changed a:16 to a:15.
5. Then I deleted:
i:14;s:34:"wordpress-single-file-php-gallery/";
6. Then I altered the plugin that was after it in the array to a new number -- changing
i:15;s:29:"wp-recaptcha/wp-recaptcha.php";
to
i:14;s:29:"wp-recaptcha/wp-recaptcha.php";
7. Then I saved my changes, fearing that I'd borked the MySQL database, but so far it seems to have merely removed the Single File plugin.
I can't guarantee this technique will work for others, but I post it here for anyone else like me who is annoyed with the WordPress Single File PHP Gallery plugin (or some other misbehaving plugin) not properly UNregistering itself.