I wouldn't. I would book the CX and change it to EK later if something becomes available.
Below is EK's JFK-DXB F and J availability, filtered to only A380s from 01/04 until end of EK schedule (currently 06/05). Z class is F, D class is J.
Code:
296 WE 01APR 0000
1 EK 204 D6 /JFK 4 DXB 3 1120 0750+1E0/388 12:30
2 EK 202 D4 /JFK 4 DXB 3 2300 1945+1E0/388 12:45
297 TH 02APR 0000
1 EK 204 Z2 /JFK 4 DXB 3 1120 0750+1E0/388 12:30
301 MO 06APR 0000
1 EK 204 D4 /JFK 4 DXB 3 1120 0750+1E0/388 12:30
2 EK 202 D4 /JFK 4 DXB 3 2300 1945+1E0/388 12:45
302 TU 07APR 0000
1 EK 204 D4 /JFK 4 DXB 3 1120 0750+1E0/388 12:30
2 EK 202 D4 /JFK 4 DXB 3 2300 1945+1E0/388 12:45
303 WE 08APR 0000
1 EK 204 D4 /JFK 4 DXB 3 1120 0750+1E0/388 12:30
2 EK 202 D4 /JFK 4 DXB 3 2300 1945+1E0/388 12:45
308 MO 13APR 0000
1 EK 204 D4 /JFK 4 DXB 3 1120 0750+1E0/388 12:30
2 EK 206 D4 /JFK 4 DXB 3 2220 2210+1E1/388 15:50
309 TU 14APR 0000
1 EK 204 D4 /JFK 4 DXB 3 1120 0750+1E0/388 12:30
2 EK 202 D4 /JFK 4 DXB 3 2300 1945+1E0/388 12:45
310 WE 15APR 0000
1 EK 202 D4 /JFK 4 DXB 3 2300 1945+1E0/388 12:45
315 MO 20APR 0000
1 EK 204 D4 /JFK 4 DXB 3 1120 0750+1E0/388 12:30
2 EK 202 D4 /JFK 4 DXB 3 2300 1945+1E0/388 12:45
3 EK 206 D3 /JFK 4 DXB 3 2220 2210+1E1/388 15:50
316 TU 21APR 0000
1 EK 204 D4 /JFK 4 DXB 3 1120 0750+1E0/388 12:30
2 EK 202 D4 /JFK 4 DXB 3 2300 1945+1E0/388 12:45
3 EK 206 D4 /JFK 4 DXB 3 2220 2210+1E1/388 15:50
317 WE 22APR 0000
1 EK 204 D4 /JFK 4 DXB 3 1120 0750+1E0/388 12:30
2 EK 202 D4 /JFK 4 DXB 3 2300 1945+1E0/388 12:45
3 EK 206 D4 /JFK 4 DXB 3 2220 2210+1E1/388 15:50
322 MO 27APR 0000
1 EK 204 D4 /JFK 4 DXB 3 1120 0750+1E0/388 12:30
323 TU 28APR 0000
1 EK 204 D4 /JFK 4 DXB 3 1120 0750+1E0/388 12:30
2 EK 202 D4 /JFK 4 DXB 3 2300 1945+1E0/388 12:45
324 WE 29APR 0000
1 EK 204 D4 /JFK 4 DXB 3 1120 0750+1E0/388 12:30
329 MO 04MAY 0000
1 EK 204 D4 /JFK 4 DXB 3 1120 0750+1E0/388 12:30
330 TU 05MAY 0000
1 EK 204 D4 /JFK 4 DXB 3 1120 0750+1E0/388 12:30
331 WE 06MAY 0000
1 EK 204 D4 /JFK 4 DXB 3 1120 0750+1E0/388 12:30
As you can see the last date with F is 02/04.