Are you looking to maximize string lifespan, regardless of playability/feel? For super long lasting strings, I would choose a thick string like BG-65 and string at a low tension (20 pounds or so). I don't think the stringing pattern makes much of a difference; can someone more experienced correct me if I'm wrong?
I have never heard of ashaway and Carlton. Neither did I know that Yonex and li Ning also sell badminton strings. Any string you really want to recommend for maximum and excellent Durability?
Yonex BG65 is considered the 'default' string to use. Personally I recommend Carlton Xelerate67 for tensions under 10kg, and have gotten lots of positive reviews. Ashaway has the Flex21 which would probably survive the apocalypse, or the MicroLegend XL is actually a nicer string.