Generally the months that I was able to sleep a lot I found I was getting better faster. I would say that I slept about 12 hours every night and had naps throughout the day, especially if I did a lot. I would take advantage of your sleepiness. It does help to get out a bit though, to keep your spirits up

I guess they say that your body only heals itself when you are in REM stage sleep, like you mentioned.

But 2 am to 3pm? what is your normal night sleeping schedule? It is good to have some consistency so your body doesn't have to work too hard.

hope you feel better.