The sleep deficit
is a
real thing, though I think it applies to shorter periods of time than the six months you're referencing.
You might try downloading a sleep monitoring / progression alarm app on your phone (I have one called sleep time). Good ones will monitor how well you sleep and try to wake you in accordance with the end of a natural cycle rather than an arbitrary wake-up time.
The science behind sleep shows that the brain operates in roughly 90-minute cycles during sleep, and if you're trying to wake up in the middle of one of those, it's tough, regardless of how much sleep you've gotten. It's why you can feel refreshed after a 10-minute snooze -- your body never enters a deep sleep -- but like a wreck if you nap for 30 minutes. At that point, you might as well put in a full hour-and-a-half.
So try to sleep for 4.5, 6 or 7.5 hours rather than the vaunted 8 hours.