I am guessing Super First Class is in reference to EK's JFK-MXP route but as you want more flights instead of premium flights it doesn't really matter.

When doing searches for award tickets it's a good idea to do the general search of your actual origin city to destination but one should also look at the various gateway cities of the program airline and the partners as that is the longer part. PE cabins tend to be small which means smaller availability. AA currently doesn't allow its own PE seats to be reserved for awards or upgrades since the fleet is quite mixed now and it can lead to a big headache for both AA & travelers when schedules change. As it rolls out to more of the fleet it will become available.

For regular economy I am seeing plenty of availability to Rome. Coming back is mostly BA or less than ideal routings when it comes to One World. But if you walk over to Star Alliance you'll find plenty of options.
Booking two sets of 1-way awards is very common.