Yep, it's a busy route but not all dates are slammed. The 21st for example shows:

BA 55: F/8 A/8 C/9 D/9 R/9 I/5 Y/9 B/9 H/9 K/9 M/9 L/9 V/9 S/5 Q/0 G/0 J/9 W/4 E/0 T/0 N/1 O/0

BA57: F/9 A/9 C/9 D/7 R/0 I/0 Y/9 B/9 H/9 K/9 M/9 L/9 V/8 S/6 Q/0 G/0 J/9 W/6 E/0 T/0 N/1 O/0

And other dates I've been monitoring have gone out with similar figures and no reward seats.