An interesting conversation. I am certainly not an expert on the methodology of securing the proper documentation in Italy, but having lived in a few countries - soon to be a fifth in Europe - I've experienced various systems. For us, the most difficult country was by far Italy. Our documentation process took an intolerable amount of time, effort, and money. We learned all the roadblocks to being "fully documented" the hard way. At one point, even though she had no papers... my wife was paying Italian taxes. Still haven't figured out how that worked?
To get our initial set of documentation to remain legally in the country more than 90 days took us about 13 months. And in the end, we had to hire Italian lawyers to secure the proper documentation (this, coupled with a trip to the Italian Miami-based Consulate). There were different levels of documentation when we lived there and each provided different privileges - like being able to purchase and register an automobile.
We both opened bank accounts in Italy before we had documentation to stay. That took us few weeks, a lease, etc.
We were IN Itay before we attempted to open back accounts (in all other countries we've opened accounts BEFORE we moved to those countries - Not sure if we could have done that in Italy as we did not try). Living overseas we are sensitive to how much money we have in our open accounts in Italy, Austria, and Denmark and what we carry back and forth to/from the States.
We have left and entered the USA multiple times with one-way tickets. With our US passport, it's been no issue for us coming into Europe. We sometimes purchase heavily discounted one-way flights - some great options! I know years ago this was an issue - and soon may return due to the refugee issues - but as of late, it has not been a stumbling block for us on our 2-3 trips to the USA each year.
I've not heard of anyone doing a long-term "home-exchange." I would think that would be a limited window of opportunity.
I would imagine that EACH effort to process a long-term stay in Italy would be unique. Not just for the national requirements but also the local (say Lazio restrictions for a move to Rome compared to the interpretation of those same laws in Florence). Probably no different than the difference between the interpretations by the Miami Consulate vs. the San Franciso consulate. And that would be the first place to start - at your assigned Consulate office.
In all the countries we've lived, Denmark and Austria were the easiest for us to secure visas. Denmark was a few hours; Austria about 2 weeks. We were approved for a long-term visa in France after about 3 weeks but never moved there. We've also had to RENEW our visas each year. Again, Italy was the most difficult, the most bureaucratic. Austria, then Denmark were the easiest.
These are just our experiences - and having sat in a few cafes listening to other expat visa stores - yours' will be different. Their's certainly were - and we were living in the same country! Our next country is The Netherlands and we've already started our process of securing an apt, setting up bank accounts, and of course, getting a visa. So start with the Italian consulate and thoroughly read the materials they provide. and ask a lot of questions. If you're able to go to Florence before you move - ask the local officials their interpretation. Good Luck!