Damn, I tested it on my mother's tablet and on my android phone and it seemed to work ok. Seems that you can never be sure about mobile devices :/
I think that I'm going to use text files to dump everything there is in the #combat div. If that works without too much hussle (as I need to initialize the jQuery sortable after loading), it's the simplest solution. Cookie would work, too, but that way you can't have multiple encounters stored in your pc prepared for your session.