Alex, your plan sounds pretty good. I hiked from Jinshanling to Simatai with the Great Wall Adventure Club:
http://greatwalladventure.com/aboutus.htm
I was able to cover Tiananmen Square, the Forbidden City, and the Summer Palace in one day. I woke up early in the morning and travelled everywhere by bus or metro.
You may also want to check
Confucius' Top Ten Tips on How to Do Beijing:
http://members.virtualtourist.com/m/tt/363ee/#TL