We are also discussing the legality of an EOSID, see the question in the title. So I commented on the notion that a PAN does not allow you to deviate from the route.
I fully agree with you, as you can read in my prior posts, that your intentions should be made clear as soon and as urgently as required, but I question the assertion that a MAYDAY would allow you to do more than a PAN. PAN and MAYDAYs are (very effective) attention getters, not legal vehicles.
If, like in your ‘Paris at 9AM’ scenario you think a MAYDAY is the best way to get the necessary attention from sub standard controllers, then by all means. But isn’t that subject to your trust in the Paris controllers, and not per se the legality of a MAYDAY call? Exactly the same legal outcome can be achieved with a PAN call: PAN PAN, PAN PAN, PAN PAN, engine failure, flying straight ahead for twenty miles, standby for further intentions.