EvoPsych also rarely finds any genetic correlation to a behavior

This is a ridiculous standard. The author presumably has no problem with using evolution to describe non-psycological traits. No one, say, demends we find the "trunk gene" before talking about why elephants evolved trunks.

More problematic still is the rarity of ever even acknowledging the need to rule out accidental (byproduct) explanations of a behavior

It's called Ockham's razor. If a behavior has beneficial (to the individual) effect X, it having evolved for that purpose is a more parsimonious explanation than to having evolved for reason Y that just happens to correlate with X.

The evidence actually suggests human evolution may operate at a faster pace than EvoPsych requires, such that its assumption of ancient environments being wholly determinative of present biology is false.

EvoPsychs are perfectly willing to explain traits using more recent enviroments when the evidence warrants it. Of course, Richard Carrier probably considers those parts "abuse of EvoPsych for purposes of racism". After all if a trait evolved after the human populations diverged, it probably didn't evolve the same way in all populations.

“Neuroscientists have been aware since the 1980s that the human brain has too much architectural complexity for it to be plausible that genes specify its wiring in detail,”

Amazing how the Creationists' "argument from complexity" suddenly becomes respectable when applied to psycological traits specifically.