Hi Aisha,
I agree that the best way to learn a language is to live in a country where it is spoken as a native language or as the 'adage' goes, marry it (sleep with it).
By circumstance, I speak 4 languages (one of which I married) in various degrees of fluency and read one more (I can't speak Swedish but due to my knowledge of Danish, understand it). Within months of learning Danish and when I was just beginning to be fluent;), I had to learn Spanish (for a post). I thought it was too soon but afterwards realized that the 2 languages are totally different, there was no room for confusion. You can say I learned my basic Spanish in Danish (does that make sense ) I keep my Danish by being active in the Danish community here.
My son (13 yo) on the other hand speaks 5 languages fluently and has no problem switching from one to the other, except in writing. Since Danish and Swedish are so close, he sometimes would use a word spelled in Swedish in the middle of his Danish sentence and vice versa (He's Danish / Filipino but studies in the Swedish School here in Nicaragua). I also know someone who injects Italian words into his Spanish but am not sure if he does it deliberately.
Some people have a head for languages and I don't know how they do it. We have friends who speak 5 or more languages fluently (effortlessly), though I'm nowhere near their ability to learn languages, the one thing we have in common is that we all learned them at post. The key I think is immersion - to be totally immersed in the language - the Ministry sends us to appropriate countries to study depending on what type of Spanish we need to learn (in our case, Costa Rica)- ex. Spanish in Central America is different from South America and Castellano in pronunciation, accent, vocabulary, etc. You may want to think about studying in Italy (since it's one of your main interests anyway) while keeping French (speaking) company, that way you still speak French and do everything else in Italian. In my experience, everywhere I go, there is always a big French (speaking) community. I would love to have a reason (like yours) to live in Italy for awhile.
I must admit your plan also sounds solid and as there doesn't seem to be any rush to learn Italian (slowly and steadily), why not strengthen your French (some more) by giving yourself time in Montreal prior to enrolling in language school, that way it would be harder to be confused unlike when it's still so fresh. As long as you regularly speak both languages, you will still end up with both. Your knowledge of French would surely help you learn Italian. Goodluck.