tl;dr version - make public quests not be public quests, and ignore all of the problems that would come into play that I failed to account for.

The way to make public quests not have the same problems they have in every MMO that has them is to not put public quests in your game in the first place. For every method people come up with to try to make them interesting, balanced, challenging, etc., there is a corresponding exploit/grief/problem. They are an inherently flawed mechanic that has never served any purpose other than to provide the illusion of dynamic content to try to disguise grind.