you dont want more than the one whm trust. they won't cure you while not engaged and you won't engage anyway. If you do, with the game giving you a stupid delay before you can start swinging and turn to the mob if you messed up in the panic, it'll be too late.
Kupofried for the extra exp/CP
Star Sybile is a must have for the extra mab.
moogle for the refresh
one whm trust for when you engage every 30 min for the recast of pro/shell
maybe the chocobo for the bit of regen.
no other bubble is of any interest for a blu cleave. extra chr is not needed.
what you need though is the unbridled learning spell named "carcharian verve". it comes from the shark WKR. that spell is a must have, it'll give you a 100% aquaveil effect for 22 min straigh (bit less if no jp or anything) that garenty no spell interruption at all save from a stun spell/move.
to luno: was the number 5 a typo? or did you really meant 5 mobs? i think an avergae geard blu will easily be able to handle half the dragon/puks and a well geared one can most likely handle nearly all of them. (DT gear in your idle/running set helps. occulation helps. cocoon helps. tusk barrier helps)
of course casting spell like floe or entomb as your first spell can matter in your survivability. but keep in mind that these mobs are only lv 107 ish and you are 119 with lots of evasion and all so it shouldnt be that dangerous.
another thing : if you feel a bit weak on your spell and you can't one-shot them, you should open your cleave with "Burst Afinity" then your aoe. that will increase the potency of teh cast by a lot. (as a reminder some AF enhance burst afinity)
and last, specifically on the puks/dragon, dont use wind based nukes... they dont cure unlike most other puks but they do take near no dmg.
now, if you want to keep up the chain, groups of 10-15 mobs max is what you want. train, kill, cure. go to the next group. that way you shld be able to keep up the chain easily enough.
there, i hope i didnt bore you too much.