I was told last month that work is progressing on schedule, so it still looks like April. Of course, I've never seen any construction work in Italy get finished on schedule, except when I remodeled my apartment. ^

For that matter, I hardly ever see big public construction projects in the US finish on schedule, unless there are huge early completion bonuses.

Anyway, worst case your flight will go to Pisa instead- and PSA is a much nicer airport, only adds about an hour to your time to downtown FLR.