When I took the GRE, I think my exam time was either 12:00pm or 1:00pm. Obviously the exam was not as long as the MCAT (I don't think it was? Maybe I'm remembering it wrong,) but I think if you aren't a morning person, than taking an afternoon exam is not a bad idea. However, do try and wake up a good period of time before the exam, have a solid breakfast (not so big that you'll need to evacuate your bowels in the middle of the exam,) but one that will satiate you long enough so that you aren't distracted by hunger pangs during the exam.
Also, something else I did on test day before I went to the testing site to sit for the GRE: I did about 10 - 15 math problems, to get my circuits going and prime myself for the exam. I don't know if this is pedagogically founded or not, but it definitely did not feel like I was going into the exam cold; definitely served as a good pre-test warm up. Thinking about doing the same the morning of test day, maybe like 6 BS passages, 6 PS passages, and a verbal passage or two.
Best of Luck!