For gaol/upheaval, I hard cast Flare on Titan so that it hits both Titan and the close Gaol as it spawns for extra damage. Then just Transpose, get knocked back, and Swift + Blizzard 3 the other Gaol to continue your rotation.

Pre-cast Sprint during your Fire rotation when you are expecting plumes. The faster you get out, the faster you get back to casting.

Firestarter and Thundercloud procs = mobility. If you get a proc and plumes are coming up, save it so you can cast it while dodging plumes.

Manawall is best used during Circle bombs in heart phase, X bombs during adds phase, or row bombs during the final phase. Use it on whichever pattern tends to give you problems.

If killing the heart isn't a problem, save your CDs for a fully-buffed 2x Flare on the Titan Egis. At the start of the final phase, start your fire rotation on Titan and wait for the OT to get into position. Pop Raging + Quelling + Int Pot and hard cast Flare on the adds. Immediately hit Convert and Swiftcast + Flare again. This should get both adds under 50% by yourself and is one of the main reasons to bring a BLM over other DDs in this fight.

On the second cycle, quelling strikes should be up but other CDs will not. Just use standard Fire rotations and be sure to use a single Swiftcast + Flare while dodging bombs followed by Transpose. In general, Flare + Transpose is best used right before periods of high mobility since you aren't gonna be able to cast anything other than Scathe anyway.

If a party wants you to use mage LB, save it for the second cycle when you can't do 2x Flare. Make sure it hits Titan too.