Hey, 3,000 words is a fine stretch of work! Surely that's one short story in itself? Or nearly?
As for sleep, manipulating it can have interesting effects. One of our lecturers at university, when discussing "trans-rational poetry" (yes, I know), said such poetry was often composed "under the effect of drink or drugs... or lack of sleep, which is cheaper!" I found that the unavoidable lack of sleep during university occasionally seemed to push REM creativity/idea-processing into waking life, and I attribute some bursts of quite heady inspiration to this. More recently, when DS was born, I was getting so little, broken, sleep that dreams were bleeding into waking life as hallucinations (not quite as scary as it sounds, nor as interesting; it was mostly about feeding).
So if you can't get the sleep, do try writing under the influence. Even if it needs heavy editing or chucking out later, you might make a few breakthroughs at the most and make rapid progress through the tedious stuff at the least.
Please don't think I'm a complete flake, or someone in search of drug alternatives - I don't lose sleep deliberately (it's far too enjoyable, and dreaming is far too necessary for sanity and also learning) - but it is possible to use sleeplessness for your purposes, rather than being battered by it!
Now, sweet dreams, and back to work tomorrow! Night, all.