Do you wanna take some time and go over the class with some of us in game? I'm not the greatest BLM but I don't even drop my AF or UI in the latest extreme fights and you gotta move in those. Lots of movement and out of instacasts? Transpose to UI, Scathe, use umbral soul to get everything back up. Plus the cast of F3 or B3 while in full stacks of the opposite is pretty quick, so you need a quick cast to up the tick do that. You gotta use sharpcast better. Thunder takes priority but having that backup F3 will help uptime immensely during moving phases. If there is a long animation that makes the boss invul, then umbral soul and restart your opener when they are targetable again. (These aren't the best but they are something)

Most of the time, if you do your opener right, ley lines lasts past the first movement mechanic so you can zip back to it and keep casting.

"So many times i've Switched to Ice and cast Ice 3 > Ice 4 only to still be at 6000 mp"
Did you use UI Paradox? By then you should have full mp. Also use UI Paradox as a movement skill during those mechanics.