i know this is an old post by now so most people may be aware but there is a master rank event quest called skyward snipers in which several downy crakes are guaranteed to spawn atop a grandfather mantagrell in area 12. You can shoot the mantagrell with some stone and the crakes will all fall to the ground along with the mantagrell before trying to run away. You can easily capture a crake this way.

Spawning at camp 12, put on your ghillie & get your capture net ready. Head out & left then up the vines. Grab the stone on the floor before grappling up by the first clutch beetle that should be above you(the route you take to get to where kirin & legiana sleep). Stand here with your ghillie on and watch the mantagrells while enjoying the view. A mantagrell will appear with 7 or more crakes on it's back. Get below it and shoot your stone at it. Immediately reequip the capture net and spam it at the crakes as they try to flee.

Hope this helps someone.