Hi Tom
Sorry for the delay getting back to you, I spent quite a bit of time testing because I wanted to be clear on what you can and cannot do in this situation.
What I'm not clear about from your question is where you are trying to add your parametric search.
I had no problems recreating your scenario and adding the parametric search to a dedicated static page. I'll run through the steps below if you have had problems doing this so you can see if anything jumps out as different from your own attempts.
But, what you cannot do is replace your archive pages with a parametric search, whether they are standard WordPress archives or WooCommerce archives. If that is what you are trying to do then that is why you will be having problems and you can effectively stop reading here, although there is something of a compromise which I'll describe towards the end.
Here is what I did to create the test parametric search which I added to a static page.
First, I created a few products with the product category "turned wood" with differing attributes for "wood" and "size".
I created a new parametric search View to display products. I only want to show products from my turned wood category, and to be able to add this query (which occurs before the parametric search filter) I needed to go to my Screen Options at the top of the page and indicate I want to see the Query filter section.
I then added a Product Category query filter. For the purposes of this test I am going to first manually select the turned wood category, but I'll come back to this.
Now to my parametric search filters. I add new filters for the taxonomies "wood" and "size" which are my product attributes.
I add something to the Loop section to display some output, in this case I'm just showing the product title, normally I would add more details via a Content Template.
Now my View is finished, I can add it to a page to test that it works (which it does).
The problem here is that I have selected one particular product category ('turned wood') to display on this page.
Here is one possible alternative, and depending how you set up your pages there may be others.
Instead of displaying the parametric search view directly on the static search page, you might create a new taxonomy view for your product categories and nest your parametric search view inside this one, editing the query of the parametric search view to select posts with Product Categories set by the parent Taxonomy View.
I'll stop here, there should be enough to clarify what you can and can't do, and I'll wait for your comments before trying to advise you any further.
