You should really just keep it all in one tread. But now that we are here... These quotes from the previous thread seem to be the most relevant to me..
"With the unorthodox construction method here, a membrane type might be more suitable, but could also be a bit costly."
"I would personally never trade the functionality of a swimmable, clean looking liner pool for the perceived "natural" look you are trying to achieve. That structure will leak without a liner.....practically guaranteed."
No one has mentioned that you have no idea on how that floor was prepped or poured. Once you add all the weight of the water it could very well move. Not to mention the likely hood of the walls moving or delaminating as well. A flexible coat would seem to be a must.
What are the issues that would make a liner fail?