I work in the corporate world and we've recently moved to a Y only policy too - it caused a bit of a shockwave with some of the executives but it's saved a ridiculous amount of money. Groups of 10 who were making 4 annual trips between Houston and London all travelling in Y has cut about 80% from the travel costs.
It's all very deliberate - the policy is forcing people to question whether it's really worth travelling. People are deciding that a video conference session is preferable to a long haul Y flight.
I've recently booked a flight with work and paid the difference to get to W (~£75 so a very good rate).
Could you push the J option on medical grounds? Perhaps a note from the doctor to support it may help the cause?