Since it's something that happens rarely, you could let the player download a file on their computer with the data you need and then give the option to load it with the new game.
It could be a JSON from an Array for example.
Unfortunately, for me, it's not something that happens rarely. I want to run a beta and a stable version.
Being forced to have unique data for each version is more than disappointing, in my opinion.
R0J0hound - I am currently doing it via a website in the form of:
beta.myawesomegame.com and stable.myawesomegame.com and it's not working, sadly :(
I also tried doing it manually, with At Start of Layout - localStorage.setItem('key1', 1337);
And this did nothing either. I can still see my original localstorage.
Shame. This seems to be a pretty significant restriction on something I feel people should have access to.