Yes, I see that you're targeting mid-July. But one thing that can broaden your options is if you can go before most U.S. schools close for summer (or after they start back up again. An early June departure will present more options for awards or reduced prices (though not for full-fare business class), and will also result in smaller crowds when you get there (there will still be crowds, just not as bad as July and August). And especially in Rome, early June would certainly feel like summer, not spring.