Even at 40Hz, the flashing was slowly getting worse and worse over time. I was usually able to adjust the screen angle to make it go away, and I thought, Hmmm...

I took the back off and tried pressing down on all the ribbon cables I could find to make sure they were properly seated. Put the cover back on, and, Voila! No more flashing. Woot!

I guess the ribbon cable for the screen wasn't making good enough contact (though I didn't find one that specifically said "Display" or something like that).

I'll try 60Hz again sometime.

Fingers crossed that it stays fixed!

Cheers,
Scott.