Is there any simple wordpress search template that works with existing searchforms?

Widget content is stored in the $wpdb->options table as serialized data. You can search that with SQL because to SQL serialized data is just a string.

SELECT option_value FROM {$wpdb->options} WHERE meta_value LIKE "something"

But…

  • The table is not indexed for that kind of search
  • Searching serialized data is dicey anyway
  • And I have no idea how you are going to associate the widgets with
    the pages. That does no happen by default and you have not answered
    my question about that point.

Put together you aren’t going to have a very efficient query and once you jump through hoops to associate the widgets and pages/posts it is going to be even less efficient still.

Sorry, but the decision to build the site the way you have was badly flawed.