Does 10:00-02:00 line up better with your usual sleep cycle? The body's natural rhythm is very slow to change, and what it is normally set to will still make itself felt whenever you deviate from it, even if you had gotten enough sleep that day...

So if you're normally asleep between 02:00 and 06:00, your body remembers that on the days when you're awake during those 4 hours, and even if you've already gotten plenty of sleep (or at least, the amount of sleep you usually get) prior to starting your "day", your body still knows that it's supposed to be asleep, and you'll feel tired...