First and foremost, do NOT push yourself past your breaking point. Don't be that guy....
I've been unfortunate to have driven under some seriously extreme conditions and do have a couple of tips
Usually tiredness related to driving for me atleast, is more associated with boredom than anything.
With that, I found having snack food like beef jerky to keep your mind and body doing things really helps.
Another couple of things are bring the handy dental floss sticks that you can use with one hand. This will keep your mind going, and you should be doing it anyways ( =
This one may sound odd, but it helped me on rough nights..... I picked up a metal extendable back scratcher and would scratch my head, my back, arms, whatever I needed to in order to keep my senses sharp.
But seriously, an 18 hour push is pretty ridiculous for someone who isn't used to that. I had many 30+ hour days while working for my former company, but believe me, I was seasoned for it and it was still stupid.
So really you should plan for a nap in here, your chances of dry running an 18 hour trip starting at 1pm is almost zero so don't try it.
If you don't want to actually lay down and sleep, 30 minute naps are the best way to go. Any more and you go into official sleep mode and you won't recover but 30 minutes is the most affective nap time in the driving world.
I'm giving you advice but I can't express it enough, do not make a stupid mistake and fall asleep at the wheel. Life is short enough as it is, don't shorten it due to being impatient.
"When I do good, I feel good; when I do bad, I feel bad. That’s my religion." - Abraham Lincoln