According to what I had read, I forgot the name of the article, it's best to rest or sleep around 10 pm to 2am because that's when your body can best repair itself. Then, you could wake up to do some work around 2am till 4am and take another nap! I tried this several times, the body clock responded nicely.

It's a bit like cats nap. I do hope you put your priority on your health first!
By the way, you are trying to beat technology! They are not negotiable, follow the rules! Ouch!
Hope your health will be on top form soon.
Cheers.