I've changed (fixed) these search functions in my fork so that clicking the boxes do not change how the drop down lists work, but just adds the ability to search by keyword. I also have an autocomplete feature so that the search matches are displayed after each key is typed. And I have also enabled the enter key universally, which is often (perhaps always?) discarded in FA. So the following advice I have might not work in vanilla FA.
But try this:
1. Comment out the following code in ui_lists.php:
/*
if ($txt == '') {
if ($spec_option === false && $selected_id == array())
$limit = ' LIMIT 1';
else
$opts['where'][] = $valfield . "=". db_escape(get_post($name, $spec_id));
}
else
*/
Then your drop down lists should still work with the boxes checked.
2. After typing in the search box, try the tab key, which allows ajax to update the page. The matched search items would then appear in the drop down list. I believe vanilla FA matches on item number, not description.
3. For the customer/supplier lists, type a space key in the drop down list to display the search box. Enter the search text and tab should allow ajax to update the page