6. If no perfectly loving God exists, then God does not exist.
This premise just indicates that Schellenberg's personal idea or definition of what a perfectly loving God must be, doesn't exist. It doesn't logically follow that God does not exist, as there are other definitions or ideas of what a loving God is.
Some philosophers conclude that God may exist but can't be all loving, all powerful and all knowing. He can only ever be two of the three. So you could have a God who is all powerful and all knowing but doesn't care to know you. Others claim he must be unlimited in order for the concept to have any real explanatory power.
Any attempt at providing evidence for the existence of God, depends upon getting the right definition of who or what God is, correct first.