So after finding out that our plane had already departed, we decided to purchase a new ticket on the spot for the next flight out. It's really not economical to do this, and I don't recommend anyone doing the same unless you really have to. The original airline we had originally booked with (HK Airlines) would have charged to change flight times anyways but their next one wouldn't be available till many hours later so it wouldn't work for us. (HK Airlines actually has a reputation for having lots of delayed flights...this was the ONE time I really wished it happened to us).
We decided on buying new tickets because our Beijing guide was already fully booked on the other days we were there, and we wanted to make the most of what's left for the day. So the next departing flight was via Air China (within the next hour); not to be confused with China Airline which I really like. Air China's staff was really nice, but the planes were really old school (the type with CRT monitors dangling from the ceiling).
Once we sorted our new flight details, I got in-touch with our guide and they suggested that we go to Mutianyu instead of Jingshanling, as we would not make it otherwise. It turned out to be a good compromise as we could still catch the sunset on the Wall, and still see parts that were original.
We landed after 2pm+ in the afternoon. But after being picked up at the airport and being whisked away to the Wall, there was still about 1 1/2-2 hours drive before arriving. The good news is there were actually blue skies (for the next day as well). The bad news was we were running on no sleep.
Going to the Wall was never really high on my list, because it didn't seem all that interesting in pictures. But, standing on the Wall in person makes me overcome with emotions. I was kind of in disbelief for a moment when it hit me that something so massive was possible. I tried to imagine how the Chinese soldiers must have felt when they were stationed here. Then sadness dawn on me when it hit how many lives were lost during it's construction.
Overall, I'm really glad to have visited. It was quite a profound and memorable experience.
The weather was great as well so I couldn't ask for more.