I’ve tried to get a better idea of your workflow but the site URL you’ve shared doesn’t seem to be loading as expected on my end. It’s tough to say without seeing your exact workflow but would setting the WooCommerce Out of Stock Product Visibility to Hidden work for your use-case?
This way the product (form) is automatically hidden when the stock level is 0. If this won’t work for you, please can you submit a ticket via our support form so that we can take a closer look at the current configuration and guide you better here?