I appreciate the intent of the OP. I'm going to level my usual criticism here and then give a terse reply to some specifics.
1. There is a bounty of literature on this subject, innumerable assumptions about "naturalism" in the OP are not accurate. This literature is easy to obtain so there seems to me little reason to have braod opinions about it without consulting it.
2. When naturalist philosophers talk about these things, in print they are very careful with their language. Even in debate it is regarded as a "cheap shot" to criticize these fairly obvious linguistic concerns. To phrase these things "correctly" is linguistically cumbersome. For example:
"God, were he to exist..." or
"The concept of evil, when understood in theistic terms..."
This is language foreign to common speach which usually gets dropped in conversation. To jump at linguistic loopholes is not charitible.
Now, as a quick overview of these moral arguments (they are generally regarded as poor and not often used). You have both logical and evidential arguments. A logical argument would concluded with either god "does" or "does not" exist. An evidential argument would concluded with "probably" before either of those conclusions.
It seems to me we first have to answer the question "Do we actually have absolute moral values?" There is a great deal of equivocation on terms which goes on here. Here's another question:
If absolute moral values were to exist, how would this state of affairs be distinguished from one in which absolute moral values did not exist?
My personal argument here is lengthy and probably not productive to share. I maintain the following propositions:
1. Based off of any common definition of the phrase "absolute moral values," and were the theistic God to exist, we would not have a state of affairs in which absolute moral values obtained.
2. Given that we do not have absolute moral values under either theism or naturalism, moral values can only be absolute relative to some referance.
3. If the relative reference point is established rationally under naturlism, it could be the case that natural moral values are superior with respect to humans than theistic ones, were God to exist.
So, the naturalists contention is that the common theistic concept of absolute moral values is actual relative moral values with respect to God, were he to exist.
Several other metaphysical arguments are out there which claim that either under theism or naturalism, absolute moral values are actually platonic sort of entities in themselves which "exist" apart from either God or minds. I don't buy these, but they are out there. In short, while these arguments are rhetorically strong, there is no productive result down this path on the question of God's existance.