Many many good books on Shackleton, but I was transfixed by one about a an explorer from a couple decades earlier - George DeLong, who attempted to find the northern passage and encountered a very similar, unbelievable, expedition in the arctic.
Book is called In the Kingdom of Ice. https://www.amazon.com/Kingdom-Ice-Terrible-Voyage-Jeannette/dp/0307946916
Simmons clearly researched the shit out of that story. It really felt like is was happening way back in the wooden ship era. I also definitely got onto Google Maps to see about where they were stuck.
A non-fiction book I read recently that scratched some of the same itch was:
https://www.amazon.com/Kingdom-Ice-Terrible-Voyage-Jeannette/dp/0307946916
Hadn't heard about the tv adaptation, maybe AMC will do a good job, some of their shows are pretty decent for basic cable.
Different boat but a great read: In the Kingdom of Ice: The Grand and Terrible Polar Voyage of the USS Jeannette