One thing I can recommend right off the bat is not resting your fingers on WASD and moving your hand around keeping your fingers as close as you need. You can move by pressing both M1 and M2 down on your mouse if you really need to.

If you do use controller, BLM actually has an easy time on controller so you have nothing to fear

And finally, I'd say use Blizz 1 as a filler ability if needed. That way you reset UI3's counter and not use too much MP in the process (better chance to be at 100% MP for Fire phase)