You can unsubscribe Presto from the JS list cause it's not made on the mob and you won't get a mob staggered by doing it.
That leave
01 Steps (15 seconds)
02 VF (20 seconds)
03 WF (30 seconds)
16 Steps
22 VF
31 Steps
33 WF
42 VF
46 Steps
Time is up
61 Steps
62 VF
63 WF
a.s.o.

4x Steps, 3x VF, 2x WF = 9 JAs not 10, 11 or 12

Let's check WHM - Dia (cast 1 second, recast 5 seconds)
01 Dia
07 Dia
13 Dia
19 Dia
25 Dia
31 Dia
37 Dia
43 Dia
49 Dia
55 Dia
Time is up
10 x Dia
Let's sub RDM, BLM, DRK - Poison (cast 1 second, recast 5 seconds) and you can easily double your chances.
Put stone I into your calculation and I bet you'll get ~25 chances within 1 Minute. (And your MP pool is drained rapidely)