Hi there. I'm wanting to do something similar to this effect: http://www.fullhalloween.com/blog/wp-content/uploads/2008/09/the_frighteners.jpg 

I've been having a devil of a time figuring it out. I imagine I can use a cloth plane with the constrained parts just around the figure's face/head... but I'm running low on sleep and my brain is acting like mush rather than being useful. 

Has anybody tried anything like this? Have you had any success? What kind of settings did you use?

Not constrained.

Load cloth plane and pose it against figure face in frame 1.
At frame 20 pose figure pushing head to cloth plane. Add keyframe to clothplane.
At frame 30 scale clothplane to 110%.
In cloth room clothify clothplane.
Select edge verticles as choreographed group.
Collide against head of figure. 

Drapaks method should work

or place figure on back in frame 1. keyframe that
place cloth plane above figure.
run simulation.
pick a frame where the face is pushed through enough.
you want a fairly light , easily stretched cloth for this .

Sample with default M3 face and cloth plane from Poser props. More polygons would work better. I've set transparency 0,1 to make face visible.