Brayflox: Split the first pull into two groups if gear demands it (once people get more allagan gear you can probably do it in one). If you DO split, the key drops off the goblins in the third pack and much of the trash can be slept, so you might consider pulling first 3 and aoeing/grabbing the key, then pulling the rest to the outside of the boss area and holding them there till they get locked out.

For the first boss, your group can skip adds if dps is good enough.

After first boss, pull all three goblin packs and avoid the bird patrols. Aoe them down, wait for Brayflox to RP, then to the second boss.

For the second boss, your group can skip adds if dps is good enough.

After the second boss, pull the first three mobs, either single target the goblins to get the key or AoE all three, whichever is faster for you, grab the key, and pull the rest of the zone. If your dps is good enough or bad enough, you can LB here to save time (good enough works because you won't need LB to skip 3rd bombs on boss, bad enough works because you'll get another bar of LB during the boss, in the middle is no good and you should save the LB) . Once it's all dead, grab the key, onto the third boss.

For the third boss, handle it like usual. If your dps is good enough, you can save cds for just before he starts circling for the third time and kill him before he goes immune. If not, you should LB at that point to kill him before he goes immune. That third bomb phase is an enormous time waster; do whatever you can to avoid it.

My personal best is ~12 minutes. Somebody in my FC says they've gotten 11; people with full High Allagan kit can probably knock it down to 7-9 minutes.