I have more or less that exact problem. I get "8-9 hours" of sleep every night but I tend to wake up several times. I'm pretty much always tired no matter what I do before bed. I've tried tea, milk, no computer, reading, exercise, no dice. That's until the weekend though when I sleep bizarrely, sometimes skipping the first night of sleep entirely, sleeping a big chunk of the next days and radically correcting on Sunday night. It makes Mondays suck but at least I'm not tired all weekend like during a big chunk of the week.
Even short of polyphasic sleep, try getting between 6 and 7 hours of sleep, make yourself get up and see how that does. Often we get "sleep inertia" where your body keeps just pumping the melatonin into your system when it really doesn't need the rest. I know that aside from a polyphasic schedule, I can sleep for 8-10 hours, but anytime I do it I feel groggy all day - melatonin in the bloodstream - this has nothing to do with having enough sleep or sleep debt.
I'll try your way, maybe it'll help. Thanks!