I have no problem with the basic premise of EvoPsych -- that psychological traits, modes of human interactions, or even social organizations are "extended phenotypes" that can be subjected to natural selection. That such "phenotypes" might not have a genetic basis can be sidestepped by postulating culture, instead of genes, as vehicles of trait transmission. But the huge, seemingly intractable problem of EvoPsych is that a lot of what the field claims are post-hoc, just-so stories, with no attempt to trace out how a trait emerge.
The same problem used to occur Biological Evolution too: there used to be outlandish theories about how molluscs evolve, with biologists proposing outlandish "intermediaries", until someone called a stop to this nonsense: if you propose a intermediate stage, you must prove that it confers benefit over the preceding stage. I'm not sure if EvoPsych can take on this challenge -- to propose how a behavioral trait like shame can emerge, step by step, with each step conferring more benefits than the step before it.
When you define the entirety of human action as a product of evolutionary attrition you state all moral impulses are nothing more than arbitrary reactions. Following this line of thought would lead you to believe that morality itself is arbitrary, contrived by nature as an expedient mode of operation
Something that confers benefits to survival or reproduction is hardly "arbitrary". What EvoPsych attempts to show is exactly that at least some moral dictates are
not arbitrary: they contribute to the expansion of some human populations -- while on the other hand also shows how disregarding the same dictates can confer benefits in some cases.
If I understand you correctly, your objection are that (1) EvoPsych robs humans beings of our agency, reducing human feelings and behaviors to sheer biological processes. (2) EvoPsych deprives morality of meaning, and (3) EvoPsych proposes itself to be the grand unifying theory of all human behaviors. (1) is a hard philosophical question that I don't have a ready answer. On one hand there are always philosophers who assert that free will does not exist; people only believe in mistake that it does. On the other hand,
Neuroscience's experiments to "prove" that free will does not exist were roundly derided by philosophers. As for the question of "inner life" you mentioned in the OP, I don't think EvoPsych assume that inner life isn't real; they are just merely unconcerned with it. The notion of "inner life", like the debate of free will, is something that I don't think science can answer, and are best left to philosophers, such as those who debates whether David Chalmers's "zombie" is a coherent notion or not.
(2) is outside the scope of Science -- Science describes what
is (e.g. what forms of moral codes there are, and how they might have emerged); what those moral code
means to people is not a Science question. (3) is an often raised objection, and thankfully we've grown out of the hubris of E. O. Wilson and his Sociobiology. EvoPsych today now posit itself as one line of inquiry among many, which shows that people in that field do listen to criticism, understand their limitations, and learn to avoid grandiose claims.
I'm no materialist (if my assertion that Science doesn't hold all the answer is not clue enough), but I think that a purely materialist line of inquiry can nevertheless produce legitimate knowledge about the human condition, even if such inquiry ignores certain aspects of the human nature. I will give EvoPsych a hearing if the field follows the practice of good science, and at this moment, they still have some way to go.