I've taken the LHR-DXB flight 3 times, and of the 6 segments once I was the only pax (in 17 seat F cabin on 777), once it was overbooked and people left behind (DXB-LHR in Feb) and the rest were 2/3 full. No idea about J/Y bookings but I do think the loads vary a lot, also time of year has quite a bit to do with it (nobody in their right mind flies to DXB in July, it is incredibly hot). April is probably quite heavy load and yes, I would worry about getting D space on that flight, insist your TA give up the booking if they can't get the space confirmed now. It could become D0J9 closer to flight date.