I don't see any reason why you couldn't sleep earlier at night, perhaps 9:30pm-2am, and take a nap sometime during the day, possibly at 11am when you get home. Stick to the schedule even on the weekends, and if you still feel tired after a week or two, try adding a second nap in the late afternoon.
Nap Length: I wake up more alert if my naps are between 20 and 25 minutes long. Longer, and I wake up groggy; shorter, and I can tell I haven't slept enough.
Core Length: I feel more refreshed after the core sleep if I wake up at the end of a sleep cycle. Likewise, if something wakes me up in the middle of a sleep cycle, I'm groggy for several hours afterward. Most people's sleep cycles are ~90 minutes long, so if yours is too, you'll feel best after sleeping 90 minutes, 3 hours, 4.5 hours, or 6 hours. (Mine are 80-85 minutes long.)
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