Everywhere I read that the relationship that Krishna devotees aspire to is of eternal servitude. They make it seem like they end up being godslaves! However, in the months I've meditated with the Harinama and other Krishna mantras I felt my relationship with Him was more like a Father-son or friendship relationship. What do you think?
The servitude is linked to devotion. When you love someone with your whole heart and soul, it's natural to want to care for and serve that person. Loving God/Krishna is more special than loving a single individual- Krishna is Love itself. And furthermore, he is the Soul within every soul. So to love Krishna, to be the servant of Krishna, is to be a servant of everyone and every thing.
But it's important to be aware that devotees of Krsna often believe that each individual holds an eternal and unique relationship with him. One person might, in the eternal abode of the Lord, feel maternal/paternal toward Krishna. Another will feel like a friend. Another like a child of God. Perhaps even as a lover. So feelingthat father-son or friendship connection is completely normal and valid.