It is definately a good thing to do.
I only did it on and off the last 2 1/2 days and already got 4 of them.
I have not had any trouble getting birds from the unique missions, though you can't pick the color that way.

I can't do 14+ if I wan't to be able to maybe get the completion rewards because Lv.100 Manyus don't appear in large numbers for no reason.
Only 2 of my squads are leveled enough to take the damage more than one enemy group puts out.

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I just did one last run before bed and now I am up to five.
I am wondering if I should just collect 20 of them over the weekend and be set for 4 to 6 months.