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If these are Cornish X or another broiler type, (red broilers, colored rangers, etc.) and are the usual age for slaughter when you get them processed, they really only need to rest long enough for rigor to pass. That's 4 hours, according to most sources, overnight to be on the safe side. Whatever you can't fit in the fridge, you could pack into coolers, in ice water overnight, and freeze the next day. Even with older birds, rigor would be past by then. With those, you could age them a few days when you thaw them. Depends on how you're planning to cook them. (The older birds, not young broilers. The broilers will be tender anyway, so long as they got the 4 hours to get past rigor.) If you're gonna cook them in the crock pot, or pressure cook, I wouldn't worry about aging beyond the initial 4 hours.
We have a couple of chest freezers, each about 5 ft long, and we put about 200 pounds of pork in through the course of one day, (as we got it cut and wrapped) when we butchered pigs. We already had a lot of food in one, it was about 1/3 full, so we added to that one until it was full, then started on the other. It was all frozen solid by the next morning. the second freezer didn't have nearly as much all at once, most of it went into freezer #1.
Anyway, if you have a chest freezer, it's pretty easy to spread the packages out, so there's room for the cold air to circulate. You could put in 15 birds in the morning, wait until night, and put in the rest. Check to make sure the first batch is frozen before you add the next lot. If I had to put birds in coolers and the fridge, I'd put birds from the coolers in the freezer first. Even if not all could go in at once. Fewer coolers to keep iced while you wait.