Booking Y+ outbound, business inbound comes to $1287 and books as follows:
Outbound:
TLV-Rome: Business
Rome - NYC: Y+
Inbound:
NYC-Rome: Business
Rome-TLV: Business
Looks like that's the closest you can get to a nearly all-business ticket for the low price.
Also, if both legs are booked Y+, the TLV-Rome (and vice versa) book in Business, and it comes to $789. Food for thought...