[burtonmiller]

That was close, but here is what actually worked. You pushed me in the right direction
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include_once DIR . '/includes/adminfunctions.php';

include_once DIR . '/includes/adminfunctions_options.php';

function set_test_save_option($varname, $value)
{
$values = array($varname => $value);
save_settings($values);
}

set_test_save_option('test_saving_options_flag', 'Some Value');
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This plugin is hooked to 'admin_complete', which seems to be a safe place to modify options. So, when you change an option, this code will get fired afterwards, and the option panel will reflect your changes.