As soon as the cutscene starts after walking down the corridor, I get the usual windows CTD.

My hardware is more than sufficient and my graphics drivers are up to date.

I've tried running through the area multiple times: copying the save over to different save slots and running it on the lowest graphical and audio settings.

I've looked over the save editor and, while it allows me to exit the challenge, I'm unable to attain the badge (unless I missed an editable value)

It sounds as though you've already looked through this thread: http://www.gog.com/en/forum/psychonauts/crashes_when_trying_to_start_jumping_into_head_video_basic_braining

Have you tried all the suggested work arounds (win 98 compatibility mode, forcing VSync)?