CLE is what's killing you.

JFK/EWR-FCO nonstop in business is $3,200 (cheaper if you do a connection).

if you can fly the short CLE-JFK/EWR in coach ($250) plus the paid business int'l ($3,200), the whole thing is $3,450 with no miles out of pocket on DL or CO.

If that works for you, I would find a reward on a ticket that matches what you can find at that price and just buy it. You may need an agent to construct the revenue ticket with coach on some segments, business on others.