HiramAbif

My wife & I are flying out of FCO on Iberia departing at 7:40 AM (Terminal 3?)
Final destination on flight reservation is BOS, but is connecting in Madrid.
(Arriving in Madrid at 10:15 AM and departing Madrid at 12:45 PM)
We are US citizens & are checking 1 bag each.
Earliest Leonardo Express Train from Rome Termini station to FCO arrives at FCO terminal 3 at 5:52

I have been google-ing all things related to what time to arrive at FCO and the answers conflict.
People asking related questions who were connecting in Ansterdam, as an example, before US final destination were answered that 2 hours is sufficient since the first leg of their reservation is to another EU country.
Others answered similar questions as a blanket statement that 3 hours are needed for all international flights.

I don't understand when passport control will check passports (FCO or Madrid) or how long the line will be (based on the "connecting in Ansterdam example above) or how bad the lines for checcking bags will be.
A aslo know that time of day, day of week, month of year, and itinerary can all play a part in security lines.
I would like to take the Leonardo Express to get to the airport but that arrives there just shy of 2 hours before our flight.
In fact I had already bought tickets for that train before I started second guessing myself. Taxi's are more than double the price and that will be over & above the nonrefundable train tix.

I am asking people with experience with flights from FCO to the US that connect in EU countries for their advice on what time I need to be at FCO based on your experience
...and asking people with no experience in that matter whatsoever (and are simply guessing) but still feel a burning need to give the standard "3 hours for all international flights" to refrain.

My confusion simply lies in the conflicting answers others received for similar questions and my total lack of experience of how passengers are processed at FCO for reservations that have the US as a final destination but connect in the EU...Isn't the first leg still an international Flight? (Madrid is in a different country than Italy...and so is Amsterdam in the example above). Or is it treated differently? I simply don't want to waste my money and time for nothing...but can't afford to miss my flight. All sincere thought out and explained answers are appreciated.