NPR's January 11, 2022 episode "We Go Up Together, Or We Go Down Together" remembers the final hours of Dr. King's life through the experiences of people who were there.
NPR's page for podcast programming is: https://www.npr.org/podcasts-and-shows
Listen to the podcast episode for free and at your convenience.
Dr. King's "I've Been to the Mountaintop" speech can be found in its entirety on American Rhetoric's list of top 100 speeches. They have the text and they also have an audio recording a bit over 43 minutes in length.