I never tried it, but I don't think that makes a problem, because WebStorage and LocalStorage uses different places to store their data.
What makes you believe that ?
It uses browser storage. In the absolute, web and local storage store infos at the same place in the browser (not the cache, the storage, a dedicated space for those infos thanks to HTML5 specs).
Moreover, it shouldn't solve the problem of storage files being cleared by the OS.
I don't think using webstorage would help with the issue at hands.
If you could somehow create files on the system and read them, that could be something considered, but I doubt this will be an easy treat, especially on Apple device.
Shaming them for their awful software and asking them to comply better with HTML5 specs could be the only solution around.
But they don't seem to care a lot as per they slow release cycle which goes on breaking previous features.