On the final tentacle phase going into furious tantrum, the anomalies will not despawn. They will still be out during tantrum, and will continue to damage and annoy everyone, so you do need to kill them on the final tentacle transition.
As far as improving DPS, I think most people, including myself, find that just having 1 dps on full-time anomaly duty is sufficient. If 1 roving DPS can't get them down quick enough, then there may be larger issues. Ideally you want to your anomaly killer to be bursty and not a lot of ramp up or DoT damage.
This would be my first recommendation as well. Unless your anomaly person is doing significantly less DPS than your tentacle DPS, they should be able to keep up. Occasionally they might get slightly behind if anoms are on far sides from eachother, but they should be able to catch up. During 1st and 3rd tentacle sets they should even be able to throw the occasional damage onto the tentacle as well, once they get really good at it. During the 2nd set of tentacles it's just too much downtime from movement, and usually isn't worth it.
Another thing that might help is having any MM specced Snipers (SS specced Gunslingers) use Entrench/Hunker Down to "eat" the tentacle Slams and continue to DPS through them whenever it's up (usually every 3rd slam, give or take your DPS). With the 60% reduced AoE damage talent on that ability, it becomes very healable, especially if they make good use of their Shield Probe and Ballistic Shield.
Also if you have not already, make sure DPS are assigned to a general area of Irregularities. The sooner they finish their Irregs and can move onto the tentacle (possibly even waiting for it to spawn and slam) the better off you'll be.