Turn 4 is a job check, the kill order is easy to follow but only if everyone is good at their jobs. There should be no overflow of mobs between phases even with a lot of DL geared players, the only exception being the second dread going into the last phase.

If there is then you have a DPS problem, but that is not always the fault of DPS. Either your DPS needs to work on their rotations, or your tanks don't have them locked down fast enough which causes DPS loss. Identify which one of these it is and focus on it, I've heard tanks complain that DPS aren't letting them grab threat but the thing is that DPS has to be burning right from the start, the tank just has to deal with it. You have a WAR tank, if they are losing agro at any point they are not playing optimally. The best WAR tank I know in coil is absurd with agro generation, I can do a buffed double flare with my full i90 gear + allagan weapon and still not rip agro from a single mob.

If it is DPS then a parser would be useful to identify which one is not pulling their weight. All I can say is that your party composition is really strong for turn 4, you have equal physical and magic, really strong aoe dps, and a bard with 2 blm. Phase 4 spiders and rook should melt in record time with that composition, so the fact there are spiders left over then suggests your dps and in particular your black mages aren't playing as well as they can.