Well there's a 13.15 BA flight to ATH which allows you to connect, just about, to the Aegean hop to JTR. That may be an option. And there are direct flights from LGW at 14.25 and 16.00 on U2 and DY respectively. Alternatively VY via BCN which which gets in very late, but may be easier for BA to rebook you on themselves given the relationship.
Frankly I wouldn't give much of a hoot about J class in this situation if you want to actually get there quickly. The seats in Y and J are essentially the same whoever you end up flying.