What is the psychological advantage of having a happiness set point? If one found a way to constantly be attached to this set point, what would the advantages be (other than perpetual happiness ^^)? How could a person become grounded in a perpetual state of happiness? What specifically would pull a person out of this state? How does a person get back in if they leave?
I think you've misunderstood the set point. It's a point of balance (or imbalance) of positive and negative affect toward which a person naturally gravitates. As such, there's not much need to do anything about leaving the set point except to wait / go on living and let time, neurochemistry, and daily life do the work.
Deliberate effort is more likely to attempt to increase positive affect beyond the set point. Thus the common struggle is generally against the effect of the "hedonic treadmill" pulling oneself back down to a more neutral or discontent set point after moments of hard-won happiness. Perpetual happiness is an elusive target for almost anyone, including positive psychologists. Most positive interventions have somewhat temporary effects (again, due largely to the true nature of the set point), though the small catalog of events that induce lasting changes to happiness is growing slowly through ongoing research.
From an evolutionary perspective, advantages to this aspect of human nature might include resilience, impulse control, and stabilization of one's identity.
Plenty of theoretical literature and research exists on this topic, and it's not hard to find. E.g., see the Wikipedia page you linked in your question. I listed one of those in my answer to this question: