I do it in a few steps:
1. When chicks are born, they get shoved into a 5x11 room. That's big enough to handle a full screen of hatchlings. All the newborns are going to be at the end of the list to start. Fast and easy and then I don't have to deal with them for 6-12 months.
2. When they mature, I pause the game and destroy the pasture. Now they'll show up in the list as no-pasture. I try to keep a meeting area near the growth areas so the birds don't wander too far.
3. Assign the males to replace dead males in the tiny rooms in various corners of the fort where I keep 2-4 of each male bird. The rest of the unassigned males get assigned to the "butcher" pasture(s). Which are rooms near the butcher shop where birds await their fate.
Male peacocks get shunted off to another pasture, because I use them to replace watchtower birds when they die.
4. Assign the females, one by one, to 1x1 pastures on top of nest boxes. This is tedious, but I work either top down (using the asterisk to page down, or the slash to page up from the bottom). I count how many pages down the list I had to go before I found an unassigned female egg layer, which makes getting back to that point rather easy.
So, create 1x1 pasture, 'n', then 'N', then asterisk/slash a bunch of times to find an unassigned female. Rinse-repeat until you run out of unassigned females in the list.
If you want less work here, limit the number of alcoves and nest boxes that you're using for kitchen egg production. In which case you should do step #4 first (replace any dead egg layers), then just assign all the remaining birds to the butcher pasture. You probably only need 60-100 nest boxes to feed a large fortress, plus have plenty of lavish meals for export.
5. Wait a bit, then go to the butcher pasture, arrow over birds with the 'v' key and start marking them to be butchered (s). Repeat at the start of every season or whenever the room looks crowded.
All in all, not terribly difficult and you end up with thousands of eggs, plus a good bit of meat and leather. When the nest boxes start looking empty because birds are dying, then I lock a female into a 3x3 room with 3 nest boxes and wait for hatching.