I've recently arrived in FCO on the E31-44 gate range, had to take the people mover and go through transit security. But then I was in the non-schengen E gates area, and just walked to Piazza di Spagna. The receptionist told me that I was supposed to go to the Hangar but I asked to stay there first instead, and they let me through just fine after warning me it was a long walk.
I stayed there for quite a while working, then noticed they had showers and took the chance.I. really needed a shower but they used these... Single User paper towerls. It was unpleasant to dry off but it worked out. I finally moved to the Hangar lounge at the end of E gates and frankly, the only drawback is less warm food options. The appys are the same, and it's much brighter and feels more open.
The only plus-side I guess is since I only moved over at 3pm, there was absolutely no one at passport control. I bet I skipped the morning transatlantic arrival rush. So I'd probably do this again if I had a long layover, but not stay that long at the Pizza di Spagna.