You outlined two main problems:

1. taking out the camera ruins the moment for you because as I understand it you need too much time to take a picture

2. your photos do not reflect your rich experiences

Body-mounted cameras sound like a good solution for you since you can take both still images and videos given that you don't need superior quality of a big sensor camera and high quality output. Still images might be important for your audience because they require less time to perceive. If you need to frame better you can always unmount the camera.

The only significant disadvantage for your use case will be limited dim light capabilities. If you want higher resolution photos you also need to pay attention to whether the camera has a function of taking high resolution photos during video recording.

I also would like to point out that you might try improving your camera skills:

1. For a lot of scenarios you might capture significant part of your experience in a few photos. It of course requires some imagination and creativity. If you want to spare time you should photograph specifically the scenes which are important for your viewer.
2. It totally does not require 50 seconds to do one photo if scene is not difficult. You might improve your single shot skills. You can also use raw image format to extend your post-processing abilities to reduce time required to take a photo.

It's totally understandable that you want to experience the scene yourself first and foremost, but it might be possible that you can improve your skills to achieve that with handheld camera.