It's Not A Tumor!

Doing this as a Servant of N'Zoth makes it trivial: all the NPCs become neutral, so you can just fly from tumor to tumor and click them. It's feasible to do 340 per hour on a known circuit route if there's no disruption.

Around the Lost City of the Tol'vir in Uldum, there are about 17 spawn points of these tumors, each with the three NPCs around them. If you don't kill the mobs, the tumors respawn in the exact same spots in 3 minutes. This happens to be about the same time it takes to complete a circuit. If no one else is disturbing the mobs – such as late at night – you can complete this in 3 hours flat, once you memorize the locations of the tumors.

You do not have to be in a raid group to avoid progress on the assault - it's sufficient to just not kill the final assault boss. Once you reach 100% progress, the tumors will become less obviously visible, but will remain clickable.

Here are all the tumor spawns I've found in Vale during Assault: The Black Empire

/way 85.9, 40.8
/way 85, 36.7
/way 84.4, 48.4
/way 82.9, 57
/way 81.6, 51
/way 81.2, 41
/way 79.3, 43.6
/way 78.4, 46.6
/way 77.5, 53.4
/way 77.1, 23.2
/way 73, 21.1
/way 71.6, 57
/way 70.4, 32.5
/way 70.1, 21.5
/way 69.7, 24.4
/way 69.1, 18.8
/way 68.8, 46.1
/way 67.6, 54.3
/way 66, 47.4
/way 65.2, 27.4
/way 62, 33.1
/way 61.4, 44.7
/way 59.5, 39.6
/way 59.2, 32
/way 54.8, 56.4
/way 54.9, 42.9
/way 54.4, 32.1
/way 52.2, 65.8
/way 50.9, 64.6
/way 49, 46.7
/way 48.4, 70.2
/way 47.1, 56.5
/way 45.7, 43.5
/way 44.7, 71.3
/way 44.6, 47.1
/way 44.5, 65.6
/way 42.5, 64.2
/way 42, 61.6
/way 41.6, 38.5

Just made a raid group and went to town while on the Assault quest.

The best way I've found to do this (in Uldum):

You can do this in a party or just by yourself. Do this on a day the quest Cleansing Uldum is up. Don't hand in the quest once you have it, just keep it. It will automatically drop on daily reset though.

Go to the Akhenet Fields in Uldum (55, 51) here you can find quite a few Corruption Tumors within a close proximity. Fly up and down this field area clicking tumors. These respawn fairly quick and you can get most of these without aggroing a mob, or only aggroing one or two.

Click on these tumours over and over until you've collected 1000!