As in your case, the assessee is billing the tools to Foreign Customer, while keeping the tools for further manufacturing the final product. Billing the client means you are supplying the tools to them at that stage and therefore, transfer of ownership. Thats symbolic transfer of ownership, though the goods (tools) are still in India. If you want to raise an invoice at the tooling stage then you have to consider, symbolic transfer of ownership hence, export. And then use URP as the recipient (without inserting the GSTIN), consider the transaction to be export of goods on account of symbolic transfer of goods (Eventually assessee cannot keep the tools, he has to send it to the FC or dispose off on the direction of the FC).
May consider a different business model in these cases of design, tooling and making final product because the above view may be highly contentious by the department. You have rightly pointed that few rulings and even department has viewed this not to be an export. Logically, if this is not an export then assessee is supplying the tools to whom? Assessee just cannot supply the tools to themselves and make the final product, in such a case the assessee doesn’t even have to raise an invoice.
A proper legal opinion should be taken for all these business model. Otherwise department may create unnecessary pain.