Could one say that it is Krishnas service to enjoy?
I wouldn't say so. That's more his nature.
He is by nature the supreme enjoyer, with no one above to serve. However, the very fact that he chooses, or is compelled to serve service itself, love and devotion, is the factor that allows the perpetual motion of transcendental lila.
Within the context of his enjoying all that humanity offers Krsna, humanity is served. The stomach enjoys all the food offered to it, but the entire body is served thereby. All are served by serving the center.
I see. To be more clear, I was thinking about divine harmony and had the thought that the devotees (the many) enjoy to serve, and Krishnas (the one) service is to enjoy. But I suppose it's more a question of nature, like you said, Syamasundara.
And your answer is excellent, Swami.