So look at greased lightning it does infact state "Damage dealt and attack speed are increased". We know this in turn does change your GCD so Huton should therefor follow suit and give you a 2.1 second GCD.

This means with huton up you could get 4 - 5 attacks out of the Trick Attack buff. Which then begs the question, is Suiton --> Trick Attack --> Kasatsu --> Raiton actually wasting the trick attack buff? Would going from trick attack to aoelian edge combo actually put out more dps?