Shopify recently added an "Unlisted" status for products, which "hides products from store search and recommendations (including collections), all sales channels, internet searches and Shopify Catalog, while still allowing access via a direct URL"

EZ Exporter also now supports this new product status.  When you create a Data Settings for Product export, you should now see an option for "Unlisted" under Filters > Status:

If you need to filter based on a combination of different status values, use the Custom Filters section instead (set Filters > Status to "Any" in this case, the Custom Filters will handle the more advanced filtering):

There's also an operator "is equal to any" in the Cutom Filters where you can use a comma-separate list of values, so a shortcut is something like this: