Hmm. There may be a better way but what about a preprocess function.
I'm still really new to Drupal, so I would maybe try something like this [code may not work]:
<?phpfunction themeName_preprocess_page(&$vars, $hook) { if ((arg(0) == 'node') && (arg(1) == 'add'&& arg(2) == 'product')) { $vars['template_files'][] = 'page-node-add-product'; }}?>
Be sure to clear cache and theme registry after making new preprocess functions.