I've downloaded the installation files twice using the GoG Downloader, and the NWN Installer tells me that both the .bin files are corrupt. Is there a problem at the source of these files? Is it the downloader that's corrupting them, and I'll need to download each file manually?

I experienced no issue with the manual download option, so I would recommend trying that.

In the "Download using browser" option field, the second .bin field is projected to be 162MB, but the file I download is actually 255MB. The first .bin file is still the projected 2GB.

That is perhaps a result of the recent update to the files to fix the missing game data that previously required people to additionally download the critical rebuild patch to get everything; it's possible those projected numbers have not been updated to reflect the new files.