Made a bit of testing for the saving stuff.
On Chrome, it looks like it keeps the save even after closing the browser, which is good. It still does not make me return to the same tile though, but at the beginning of the "group of three tiles", and the events/encounters are different.
The compendium works on chrome, but on safari it does not. It is not linked to my "LaserQuacker" account, but to the browser itself, so I can't port data from chrome to safari.
I did not have time to try a long run with Chrome to see if there is still the "ran out of memory" problem, but I'll give it a try when I can.