I'd be doing everything I could to have the tickets reissued as proper J before arriving at the airport. There is an incredibly high chance that an obscure airline operating 2 flights a week from a secondary airport will not have briefed all of their staff properly and the request will squarely fall into the 'too hard/CBF' category.
I'd be amazed if this airline even has an airport manager for LGW, surely they just outsource everything to a Dnata type company who wouldnt have a clue of the directive, let alone the power to override a booking and change a fare class. Even with the email from the airline in your hands I'd expect they'd simply say to you 'we dont know anything about that and can't change it anyway'. The best you could hope for is a discretionary upgrade on the first flight. Its not like you're attending to BA service desk at LHR where there are plenty of supervisors who can do things on the spot.
I'd be very interested to hear anyones experiences at LGW.