It may be immediately beneficial to sign up for a language school, pay in advance for say, four months, then approach the authorities - letter from the school in hand - and ask for an L permit. This will likely be offered and is valid for 18 months, giving you time to get yourself settled, find a job, catch your breath.
Your partner would be wise to get the UK passport asap; it will only help the cause. Of course, nobody is really going to know if someone should remain longer than the three months a standard tourist visa allows, especially if you plan tactical trips to Italy now and then
Pleading letters are not likely to cut any mustard unless one of you are Swiss already. It's not enough to be rich and eager to live here - unless you're seriously wealthy - so perhaps a low profile would be a good tactic for the time being. Good luck.
Come down to one of our social events - see the calendar - and have a chat with some of us who've been here a while. And enjoy a beer.