I really can’t see why EK is not refunding you the fare difference. Is there a considerable amount involved? If there is perhaps a letter from your lawyer threatening legal action or as someone suggested, dispute the charge with your credit card company. I assume where you are living there is not the equivalent of a small claims court as there is in the UK?
In the meantime you have received a personal reply from the CS manager. Try calling him and discussing the matter. If as he says 39,000 miles is enough to upgrade fro J to F then fair enough I suppose, providing of course you will be flying the route again.
The reality is threats will get you nowhere and one or twp pax more or less will make no difference to them. Likewise if people are happy with EK they won’t change their preferred carrier because of the above. In fact I have an upcoming trip to the US and the EK flight out of Milan is quite convenient, well priced and chauffeur collection, so I’m not swayed by your poor experience. In fairness if I’m let down I’ll likely grumble and recall your post!
It’s a tough one and I do sympathise, but I’ve learnt that unless you carry lots of clout by way of who you are or the business you bring, you’ll be banging your head against a brick wall. Legal action or the CC route are your best bets.