the problem is only DL from JFK and US from PHL fly non-stop to VCE both using a 767 and US wont be bed-flat
to FCO (Rome) theres AA,AZ (Alitalia), DL from JFK, CO,AZ from EWR and US from PHL not sure what will be used next Aug now its usually a 767
the best would be a DL/AZ say flying NY-VCE on DL then AZ VCE-FCO and then DL or AZ FCO-NY, but as usual DL will probably want way over 200k per Biz tkt
as AZ is a Partner in SkyTeam, using AA or CO or UA or US will mean you are on your own getting to/from Rome & Venice however you decide to do it. Maybe a flight to FRA and then to VCE can be worked in but that will be like flying from NY to Dallas to Boston way out of the way and will kill most of the day on you (thats for getting between Rome & Venice)
Id probably play with say Swiss to ZRH and then to VCE (if done right you can do <24 hrs in ZRH and it doesnt count against you), then train it down to Rome or the opposite. I didnt care much for LHs biz product
EasyJet flys between FCO & VCE for very little but will get you if you are checking in bags etc etc