"so they'll just tell everyone about their new delivery service and you'll find out you're not eligible when the postie arrives"
They could probably let you know at the ordering stage - possibly even on the product details page if you're browsing Amazon while logged in - since they have your address* on file, and also a record of where they have stock of any given item. Clever things these computers.
* Obvious caveats, such as not being an Amazon customer, notwithstanding.