Which is normally fairly reasonable. Do you have any flexibility in your schedule on leaving earlier? Might be worth getting to JFK and explaining your case?
Looks like loads are reasonably tight on the later flights, but open on the earlier ones. I've checked in at JFK before and been told my flight is running late due to weather, but they've already moved me to another flight with less of a delay.
BA172 F1 A1 J0 C0 D0 R0 I0 W3 E2 T2 Y1 B0 H0 K0 M0 L0 V0 S0 N0 Q0 O0 G0
BA112 F2 A2 J9 C0 D0 R0 I0 W5 E4 T1 Y3 B3 H3 K3 M3 L0 V0 S0 N0 Q0 O0 G0
BA174 F6 A6 J7 C2 D1 R0 I0 W5 E0 T0 Y9 B9 H9 K9 M9 L9 V9 S6 N0 Q0 O6 G2
BA176 F3 A3 J6 C3 D2 R0 I0 W4 E4 T3 Y8 B6 H6 K8 M8 L8 V8 S0 N0 Q0 O0 G0
BA114 F4 A4 J2 C2 D2 R2 I2 W5 E3 T2 Y7 B7 H6 K3 M3 L3 V2 S0 N2 Q0 O0 G0
BA182 F0 A0 J1 C1 D0 R0 I0 W0 E0 T0 Y5 B4 H3 K0 M0 L0 V0 S0 N0 Q0 O0 G0