I think it might be possible to provide J with a sit-down dining experience without reducing the normal service level in the Sky Club, but it would require a lot of floor space. Just set aside another area like the upper level at SEA, the new club at DTW, the undeveloped half of the satellite lounge in BOS...
Years ago, they tried doing a sit-down meal service for J pax at JFK T4. When I checked into the SC, I got a stamp or a coupon that I handed to the waitstaff. I think something like this could be a compromise, especially when space is tight in certain airports — as is the case at JFK.