General

i think final cut + mille outdps RF (ideally) but you have to be in pretty close range so it might end up having your actual dps on bosses be about the same both ways. Green pot and SI definitely dont affect hurricane-like attacks tho, only the speed it takes to cast i think.

Decent SI + MPE green pots only speeds up the start up animation of the skill, after that it's just a fixed speed. The same thing goes for arrow blaster, and arrow blaster would increase your DPS by a ton.

Thing is... Mille Aguilles is a skill directly tied to your Phantom. Impecable Memory IV can be used on any Adventurer skill. Instead of using Rapid Fire, you could be using a buff skill like Advanced Blessing and augmenting MA's damage further than what Rapid Fire could do (also, Adv. Blessing lowers MP costs for example). Also, as someone else has mentioned, Arrow Blaster may be more effective than Rapid Fire in the long run as well. Not only is it a powerful skill on it's own, but by placing the turret down, you can rush in with MA and press the attack further.

isn't arrow platter better then both of those skills anyway?

Mille will not increase or decrease in speed. Key down skills have a fixed speed. As for DPM RF will do more damage, but compared Arrow blaster both of them are a waste of time.
Even if you can't use normal turret cuz you might get killed, the dpm of turret and mille outperforms rapid fire.

I really don't think Mille gets faster with the potion. Fairly sure "fixed speed"-skills aren't affected at all.

EDIT: After looking at your video, I'd say your Mille is as fast as mine. (Without Green Pot+ SI)