Does anybody know if there's a way to exclude a product from showing up in the products with attributes stock page?

I have a product with 4 options, but I want an unlimited quantity for all the combinations of options for this product, so in the catalog I put 10,000 as the quantity. This is a custom order product.

The problem is that when I go to products_with_attributes_stock.php I see the product with the product ID there. I don't want to populate this product with the options on this page, because it's a bunch of unecessary rows in the DB. I would prefer if this product didn't show up on this page at all.

The problem is, every time I press "Sync quantities" in the upper right corner it lists this product with a quantity of 0. I do not want this.

So I'm looking to exclude the product from this page completely. I looked in the products_with_attributes_stock table but I could not find this product ID on the page at all!