You might have better luck booking positioning flights in the US and EU and using your points to fly Iberia out of JFK or BOS. That would put you into Madrid, but the transatlantic flight would be in BC. The real down side to this (whether Iberia or not) is that your times are during peak season, so even if you find availability, there's a good chance that you won't have enough points.

This is how my wife and I when to Italy in April, just before the start of peak season, and it was really easy (and relatively cheap) to start in Venice and end in Rome from Madrid. Hopefully, you find a path forward, because Italy is magical. As Phil Rosethal says, Italy wins.