Rough Draft: First Pass.
Standard responses to the naturalistic fallacy argument in the literature:
1. Some analytic truths aren’t obvious, and truths about the nature of moral normativity are likely among such truths (cf. many mathematical truths).
2. Related to (2): Falsely assumes there are no interesting analyses, when in fact there are many (e.g., knowledge as JTB or truth-tracking theories; dispositional analyses of color, etc.). (Smith)
3. Frankena’s objection: the open question argument begs the question against analytical moral naturalism.
4. The goodness-fixing kinds response (Geach, Thomson): Moore's argument presupposes that there is such a property as goodness full-stop, but this is false; there is only goodness relative to a kind (e.g., a good knife, a good toaster, good person, etc.), and the standards of goodness are relative to the kind of thing something is. Whether a thing is good depends upon whether it performs the function of its kind well (as with functional kinds) or otherwise meets its kind's standards of correctness.
5. The argument doesn’t apply to a posteriori moral naturalism.
6. The argument's conclusion is unproblematic for non-theistic non-naturalist moral realism.
Standard responses to the is/ought gap argument in the literature:
1. Thick ethical concepts (e.g., 'cruel', 'generous', 'selfish', etc.) have inextricable components that straddle the normative/descriptive divide (cf. Foot, Williams et al.), in which case there is no sharp is/ought divide. But since Hume’s is/ought gap argument requires a sharp is/ought divide, his argument fails to show that moral normativity is problematic.
2. You can derive an ought from an is (Prior, Searle, Maitzen et al.). Here’s Maitzen’s example from his paper, “Closing the Is/Ought Gap”, Canadian Journal of Philosophy (1998):
(Bl) Some ethical sentences, standardly construed, are true.
(B2) Either no ethical sentence, standardly construed, is true, or torturing babies just for fun is morally wrong.
(B3) Torturing babies just for fun is morally wrong.
3. Neo-Aristotelian virtue ethics, non-theistic natural law theory, and non-theistic proper functionalist moral realism (Aristotle, Foot, Hursthouse, Nussbaum, Thomson, Lott et al.): You can get an ought from an is via natural biological functions, and you can get natural biological functions without an intelligent designer.
4. Related to (3): The value-first buck-passing response (Foot, Hursthouse Lott et al.): reduce moral normativity to goodness, and analyze goodness in terms of flourishing or proper function or health or… Since flourishing (or proper function or health or…) is a natural property, normativity reduces to the natural.
6. (Non-constructivist) constitutivism (Thomson, Smith): You get moral normativity from descriptive facts through goodness-fixing kinds.
7. Moral oughts reduce to instrumental/practical oughts, and instrumental oughts are naturalistically unproblematic (Williams, Railton et al.). Example: Morality is reducible to instrumental rationality from the social point of view (Railton). Relatedly: Reforming-definitions of morality (Brandt, Foot, Railton et al.): Morality is usually, but not always or necessarily, action-guiding. The contrary view was part of our intuitive, public conception of morality, but it’s a defective part. We should therefore reform our conception of morality accordingly to make it reflect the moral facts more accurately. Reject morality as a system of categorical imperatives; take morality as a system of hypothetical imperatives.
9. Analytical functionalism/network analyses (Jackson, Pettit): Normative moral properties strongly supervene on natural properties -- there are no two possible scenarios with identical descriptive properties that differ in their normative properties. This is a strong reason to think normative moral properties are identical to descriptive properties. One can assemble our normative moral platitudes, functionalize them and represent them via a purely descriptive Ramsey sentence, and then identify our normative moral properties with the descriptive properties upon which they strongly supervene, thereby reducing the normative to the descriptive (cf. D. Lewis).
10. A posteriori moral naturalism/Cornell Realism (Boyd, Brink, Sturgeon et al.): Kripke and Putnam showed that there are a posteriori necessities, since there can be two or more concepts for the same property, and (the narrow content of) neither concept entails the other. The normative facts either strongly supervene upon or are identical to certain natural facts, but these are necessities that are only knowable a posteriori. Moral truths strongly supervene upon natural truths. So by IBE, the best explanation is that those natural truths ground or constitute or are identical to the moral truths.
11. Response-dependence/projectivist accounts (e.g., Hume, Wright et al.): Moral properties are like secondary qualities. They are mind-dependent, yet generated by all normal human minds under normal conditions.
12. Non-theistic moral non-naturalism (e.g., Moore, Ross, Wielenberg, Huemer): Oughts exist at the metaphysical ground floor, and so there is no need to derive an ought from an is.
13. Expressivism (Gibbard et al.): There are no moral norms. However, facts about a given agent's practical/instrumental reasoning/planning play the role of supposed moral norms, and statements about morality can be replaced with statements about our plans/planning.
14. Fictionalism, in either its hermeneutical or revolutionary forms (Kalderon, Nolan, Restall & West, Joyce et al.): Moral norms aren't real, but we have outweighing practical reasons to act as if they are. These fictions suffice to play the role of objective moral norms.
For further reading:
Standard primers and related points of entry into the relevant metaethics literature include:
 It’s perhaps natural to think this approach is broadly Platonist, but Aristotelian accounts can take normativity to be at the ground floor as well, and to see objects generally as teleologically and thus normatively structured.