Co-existing with regular search product widget

Hi again!
I’ve set up a shop page on a staging site. I am impressed by the plugin so far. I got a feature request, or perhaps you could advice how to go about.

The shop page renders the filter (checkboxes) before the shop product archive through a shortcode call in functions.php. It’s working very well. But I want to have a regular search widget (not from your plugin) in the sidebar for visitors that want to search for specifik product by title (The search field that your plugin’s filter can show, searches for filterable (in my case) product category terms and I don’t use what since I think it’s confusing the visitor (thinking it’s a search for products)).

When I do a search for a product title with the regular search widget, the sought after products are shown AND the Filter Everything section reacts too, removing the product category terms from the collection of filter checkboxes. BUT. There is no way I can reset the shop page to a default state, short of clearing the search field and hitting enter.

Thoughts?