The thing about the sleep I imagine is like when you only get a short amount of time, your body is still full of the adrenaline it produces when you're over-tired, and it's unlikely you've had any sort of deep sleep.

You get a bit longer and it finally starts to unwind and relax and start the healing processes. The reason you feel exhausted when you get up then is because you've interrupted it in the middle of what it's doing, and it's shocked out of it and thinks "Shit, I have to switch power from healing to making and releasing energy". If you had 8 or 9 hours you'd feel better.

If you try tea and a hot bath, make sure it's herb tea or decaffeinated tea, and it might be beneficial to put in a few drops of an essential oil like lavendar, camomile marjoram or sandlewood as they all have calming, soothing and sedating qualities to them.