How can I change the Available Menus to all, programmatically, for a specific content type?
If I understand you correctly you want to change the available menus for node types when new menus are created.

You can implement hook_menu_insert to respond to new menu creation and you can use variable_set to add the new menu to the available menus for the selected node types.

E.g. this will add all new menus to the page and article node types:

function mymodule_menu_insert($menu) {
  $types = array('page', 'article');
  foreach ($types as $type) {
    $menus = variable_get('menu_options_' . $type, array());
    $menus[] = $menu['menu_name'];
    variable_set('menu_options_' . $type, $menus);
  }
}


If you already have created a bunch of custom menus, you'll basically need to call variable_set as in the example above.