I think Elayne's article makes a lot of good points on this. I also think that there are a lot of intricate side questions, starting with something as obvious as pointing out that "happiness" is not a Greek word and not the therefore not the exact word that Epicurus used, so we have to be careful of two thousand years of potential changes in shades of meaning, plus translation issues, at the very beginning.
We've had extensive discussions about this in the past and we will probably be discussing these issues as long as we remain interested in philosophy. In the end we have to try to reduce the discussion to something workable, and we know that Epicurus held "pleasure" to be the guide of life, the alpha and omega, and all that, and he did not use the word "happiness" in that context.
In trying to sum up conclusions about the relationship to happiness and pleasure it seems to me that that observation has to ultimately be the test by which we sum up Epicurean philosophy in an understandable outline.
So we have to come to grips with why "pleasure" and not "happiness" occupies the central keystone role in Epicurean philosophy.