I'm not a super experienced Randonneur with only one and a half seasons and two 600s under my reflective belt, but in my experience:
Definitely agree with the sleeping in 90 minute sleep-cycle intervals thing. You'll wake up feeling much better if you wake after a complete cycle.
Also agree with the suggestions to chew gum or nibble on something (I like Fritos). Chewing definitely helps keep you awake.
Everyone has very different needs and abilities when it comes to sleep and sleep deprivation. My wife is grumpy as heck if she doesn't get 8 hrs a night, I get by fine with a lot less. It's just how I'm wired. You really need to experiment with your own limits to know what works for you and what doesn't.
Getting in and out of controls quickly can buy you lots of sleep time. Riding fast helps too, but I think most Randos have a lot more to gain from being efficient at controls than by being faster on their bikes. Think of it this way: You only have to average 12 mph on a 600k to get 6 - 7 hrs of sleep
if you keep other control stops to 5 minutes or so.
Sleep dep hallucinations: Annoyance to be overcome, or signs to take a break?
Again, different people have different limits. On the SiR Mountain 600k last summer, I had a vivid halucination of a mountain lion beside the road getting ready to pounce on me as I approached Chinook pass at 2am on the second night (
that got some adrenaline pumping!). But even though I was halucinating, I never really came close to dozing off. As long as I kept pedalling, I felt ok. But that's just me. I know other people much smarter than I would have been sleeping in the ditch long before that point.