I reached out to a travel group that my co-worker used when she was in Beijing last year. Based on what I was thinking, here is their proposed tour itinerary, at a cost of 4400 RMB, including admission to any sites:

Day 1: Meet me at the airport with a private car and english-speaking tour guide. Go to Mutianyu (they tell me that Mutianyu stops selling tickets at 17:30 and stops admittance at 19:00, so they are planning to have someone buy my tickets, just in case, and hand them off to the driver/guide). Drive me to my hotel in Beijing after.

Day 2: Private english-speaking guide to take me around Beijing, including Tiananmen Square, Forbidden City, Hutong walking tour and Fayuan Temple. We would use public transportation.

I would then take a taxi from my hotel to the airport.

I am curious to hear feedback on the proposed itinerary and proposed cost.