OK, so all I apparently needed was another half a day.
I used the plugin: Shortcode Exec PHP, then created a shortcode for the below code:
global $wpdb;
global $current_user;
$current_user = wp_get_current_user();
return $wpdb->get_var(“SELECT field
FROM table
WHERE field
= ‘$current_user->user_login'”);
… with “output echoed” unticked.
The shortcode then easily placed in a page.
I believe I was close on a number of occasions way back, but had the quotes mixed up on the $current_user->user_login variable.
Glad that’s over. Next challenge now. Hope that might help someone else.