Sleep isn't "wasted" time. Without sleep, we'd be dysfunctional, and soon thereafter, dead.
- How can I determine the best time to sleep?
- What food to eat before sleep?
- How can I be productive all the way until I fall asleep?
- Why no sleep drug without harsh side effects?
Just a few things I'd like to see research into...
Also you're mixing up many different aspects. Feeling sleepy doesn't mean you're sleepy. Motivation is a different thing altogether.
So power through?
Getting sleepy is your brain telling you to preserve energy. Only sometimes it does that because something about the work itself bores, infuriates, disgusts, or otherwise upsets you.
That means getting "procrastination-sleepy" is your brain trying to prevent spending energy on the miniature emotional turmoil "breaking procrastination".