Rooted! Interestingly, I was able to root this machine much more quickly than my previous Windows boxes, Sauna and Monteverde. As if what I have learned so far was being put to good use. All the useful hints are already available on this forum thread.
user1: be diligent with your enumeration, I didn’t expect to find the useful bit of information there, but I did it anyway, and it’s there.
user1->user2: hunt for a hidden place
user2->root: check his group, what he can do with it, and inject the exploit