I don't think they did what they could... especially Romeo. The prince was very vocal about wanting to end the feud, and given that he had the ultimate power, Romeo could have appealed to him for help. The prince very well might have either A) talked sense into Romeo by asking him to take things slower while he approached the issue with Capulet or B) give the young couple permission to marry. Because the prince was so involved in this feud, I think an older and wiser perspective on matters could have helped both the couple and the families.
I think they did everything they could do in their era. They might have run away together, but their parents would have hunted them down, and the family feud would have gotten very nasty. In an ideal world, they might sit their parents down and try to talk sense into them, but this is not an ideal world.