How is $search_results in search-results.tpl.php generated
About theming results, you should have 2 templates: search-results.tpl.php and search-result.tpl.php (without s).

The first one allows you to theme the list, the second one (without the s) allows you to theme the results individually.

So I would advise you to use a hook to sort/filter the results the way you want (see answers from Clive and arrubiu), but use the templates to define the design you want.