During the writing phase of the checkpoint, PostgreSQL passes the dirty data to the OS. At the end, it then tells the OS to make sure that that data has actually reached disk. If your OS stored up too much dirty data in memory then it kind of freaks out once it is notified it needs to actually write that data to disk. The best solution for this may be to lower dirty_background_bytes or dirty_background_ratio so the OS doesn't store up so much trouble for itself.
Actually, I have already tuned them to different values. Test results above have been obtained with such settings for page cache:
vm.dirty_background_ratio = 5
If you have 64GB of RAM, that is 3.2GB of allowed dirty data, which is probably too much. But I think I've heard rumors that the kernel ignores settings below 5, so probably switch to dirty_background_bytes.