Got it. I had tried to use flush_rewrite_rules() on plugin activation/deactivation, as so:
function creativeworks_activate() {
// register taxonomies/post types here
flush_rewrite_rules();
}
function creativeworks_deactivate() {
flush_rewrite_rules();
}
register_activation_hook( __FILE__, 'creativeworks_activate' );
register_deactivation_hook( __FILE__, 'creativeworks_deactivate' );
…but that didn’t seem to do anything. However, when I changed the site-wide permalink options arbitrarily and saved them, then the rewrite rules were flushed successfully, and my custom post type templates started working again.
Thonks to Milo for pointing me in the right direction.