Carrying Basic Instinct into the instance is huge! That's a whole 2 second GCD right there.
I noticed that sometimes the buff took awhile to "fall off" and I tried to "catch it", but I was never successful. I started coming up with wild theories like it takes longer to fall off in the Gold Saucer, in crowded areas (I tried Limsa), various other things. I felt like saving Basic Instinct was impossible because even when I thought I had it, I'd lose it during the fade out. I'm going to have to research it again because this could save two seconds on any fight.
At least the normal should be possible. This video proves it: (not my video)
I think you have to manipulate the timing of the QTE such that you have time to deal more damage. The EX however might still be a problem for a lv 80 blue mage.
When I submitted this run I put 3m 8s as my RTA and left the IGT blank. It was supposed to be the other way around.