As a Reformed Christian, I don't see a dilemma here. Do you?
Attacks on the Christian faith come in all forms. Many educated non-believers think the way to beat God is to try to make his followers feel intellectually insecure. This is nothing new -- even Paul warned:
See to it that no one takes you captive through hollow and deceptive philosophy, which depends on human tradition and the basic principles of this world rather than on Christ.
As Christians, we stand on Biblical truth, not the cleverness of man, and thus have no reason to feel insecure about anything. So let's take the dilemma apart and peek under the hood...
We can quickly dismiss the first part of the dilemma: there can be nothing higher than God, nothing that transcends God, no separate standard to which He can be held up, indicted or shamed. Morality must somehow originate with God.
As to the second part: does God actually decree morality, or is it simply a reflection of His character?
The Ten Commandments address the rules governing two types of relationships: man's relationship with God, and man's relationship with other men. Every commandment presumes these relationships exist. Do not worship other gods. Do not murder. Do not steal. Do not covet anything of your neighbor's. These rules make no sense in a universe of one.
How about the Golden Rule?
So in everything, do to others what you would have them do to you, for this sums up the Law and the Prophets.
Again, this presupposes relationships, by explaining how to participate in good ones: treat others with the respect you would like them to grant to you.
The essence of morality appears to be relationships, and how to get them right. One could argue that even one person alone in the universe could sin against himself, but it isn't obvious how. The sins we refer to as "self-destructive" are judged bad because of their effects on others, and because they are an affront to God's gift of life -- if there was no one else to be affected, and no god to affront, what then? If the only person in the universe was an abusive drunk, he couldn't go home and beat up his wife. If he was a drug addict, he'd have no job to lose. If he was suicidal, there would be no one to mourn his passing, and no one dependent on him to suffer from his absence.
Christianity is the only religion in which not only is God eternal, but so are relationships. As Father, Son, and Holy Spirit -- Three Persons in One -- God has participated in perfect relationships from the very beginning. This means we cannot impute arbitrariness to God; He is eternal and unchanging. This means morality is not some unknown, unknowable, abstract thing hanging out there somewhere in space, nor is it a set of arbitrary dictates issued by a lonely monadic deity. Morality is the way the Father, Son, and Holy Spirit relate to each other and have related to each other for all time -- and which defines how we, as God's creatures, should relate to each other. In the Bible, whenever the Father speaks of the Son, it is with the utmost respect, deference, and love -- and likewise, when Jesus speaks of His Father and of the Holy Spirit. Their eternal relationship would not have been sustainable for more than a few minutes without the sort of loving care they take of it. They can no more afford to be arbitrary than we can afford to be arbitrary in our relationships with our spouses, children, and other loved ones. When God tells us to love one another, He is asking us to do no more than what He already does, and has done for all eternity.
To be fair to Socrates, the nature of our Triune God had not been fully revealed in his day, not even to His [the Lord's] people, the Jews. It made perfect sense for Socrates to presume that a monadic god could be arbitrary or whimsical in his decrees. (In fact, this is precisely how Islam conceives of Allah: a monadic god who changes his mind about what is right or wrong.) If God were monadic, then he would have been (at least for some period of time) the fellow we were just talking about a few paragraphs ago: the only person in existence. The very first time he created other beings, relationships would also have been created for the first time -- and hence so would morality. So much for eternal and unchanging; so much for absolute morality.
So Socrates had an excuse; those who pose the question nowadays do not. If morality is absolute, the only consistent explanation to be found is from the Bible: morality originated with our Lord. If morality is not absolute, we have no reason to worry about whether we're adhering to it, and no reason even to suppose we can know what it is. Better to pose the question to the moralistic unbeliever: if you don't believe in the Lord, why do you act as if morality exists apart from your own particular tastes, whims, and preferences? And if that's all morality is, why are others obligated to obey it? Having such frank discussions probably will not change their minds or hearts -- that's the Lord's job. But it's our job, whenever possible, to give them pause.