Thought I should post a follow up to my earlier questions, tho obviously one isolated experience is worth little...
I arrived at FCO's T5 at 08:10 for my 10:00 FCO-JFK flight in J (on a Tuesday). The place seemed almost deserted. No line for the security questioning (the "who packed your bag questions"), no line for check-in. Received both BP's (final destination was LAX), and the pass for Le Anfore. Barely a line for security (didn't notice any bodyscanners). Boarded the shuttle bus to T3 by about 08:20. Must say it was the smoothest, fastest process I've ever been through.
Re: Le Anfore, it was actually not bad. I had only tried it once b4 and I recalled it hot and crowded and noisey with a scary ladies room. This time tho it seemed airy, less crowded and suited my needs. (Had my last good coffee, some fresh and tasty cornetti - and an informative conversation with a lovely Brazilian man who educated me on the merits of ordering a caffé lungo vs the Starbuckian doppio espresso). The ladies room still scared me however.
When I arrived at the gate it was very crowded, appearing that it was a full flight. (Perhaps the majority of people arrived earlier than 08:00 and were processed b4 I got there?)
Re rrgg's FCO arrival question: I encountered no line for immigration (I was one of the first to deplane). But... the JFK-FCO was also 4 hours late to arrive which would account for the lack of pax from other carriers. (OT but noteworthy, received an unsolicited email apology and 5,000 miles from AA Cust Serv for the delayed flight).
Thank you for the information. It was really helpful!
I can't imagine the bathrooms in Le Anfore being worse than those at SJU's baggage claim area.

They shouldn't even be labeled as such.