1. Nihilism- I conclude that nihilism is true due to the inability to logically justify any moral judgement (why rape is wrong, why I should help others, etc.).
2. Emotivism- I consider this to simply be factual, as evidence seems to show that we use the emotional part of our brain when answering moral questions.
4. Relativism- True because people have varying moral systems depending on culture, etc. — Pinprick
Emotivism is a theory of moral semantics. It's not just a theory that we use the emotional part of our brains when answering moral questions, but a theory that moral claims are just expressions of emotion like "boo this" and "yay that", the likes of which are not semantically capable of being true or false.
Nihilism and relativism, meanwhile, are theories of... moral ontology, maybe? About whether and in what way any moral claims are true. The former is a subset of the other, in any case; relativism is anything non-universalist, and nihilism, being radially anti-universalist, thus cannot help but be relativist.
And emotivism entails nihilism (since according to emotivism no moral claims can be true, or false for that matter), so if you just say "emotivism" then you imply nihilism and so relativism for free.
3. Hedonism- Essentially factual just like 2. It’s obvious that we avoid pain and pursue pleasure. — Pinprick
Hedonism isn't just the view that we
do seek pleasure and avoid pain, it's the view that we
should, and so is contrary to nihilism and thus emotivism. (But it can be of either an altruistic variety, like in utilitarianism, or an egoistic variety, like people usually assume it means; and the egoistic version is thus relativist, see below).
5. Egoism- True by default. Evolutionary pressures have led us to experience pleasure when we make choices that benefit ourselves (also, helping others oftentimes helps us as well). — Pinprick
Again, egoism isn't a view about what people
do do, but what they
should do. If egoism is true, then it is
good for people to do what benefits them; and there is something that actually does
benefit them. That means nihilism, strictly speaking, can't be true (if egoism is true).
Egoism entails relativism, though, since what is good according to egoism depends on which ego you ask.
6. Pragmatism- In life, I essentially ignore all of the above and instead just try to do whatever feels right and works for the particular situation. — Pinprick
This sounds like you don't
actually agree with any of the above, since you ignore it all in practice.
I suspect what you're actually going for here is denying that there are any kind of moral facts about reality, but then in practice you still aim to do what is good. (I.e. what "works". What exactly does that mean here? There's the big question. What are we trying to do, in deciding on our moral opinions?) You just don't have any notion of how you can rigorously sort out what is good, since you can't apply the rigorous methods of sorting out what is real to morality, since morality isn't a part of reality, so you're just left with whatever you intuitively feel about it.
But maybe you could at least apply analogous methods?
I would suggest looking into non-descriptivist cognitivism, which I think will resolve that dilemma for you. It is a theory of moral semantics which holds that moral claims aren't aiming to describe facts about reality at all, much like emotivism, but that they are nevertheless cognitive claims, i.e. the likes of which are capable of being true or false in some sense or another, not just expressions of emotions that aren't even truth-apt.
This then enables universalism, but without supposing that there are some kind of weird metaphysically spooky moral features of reality that those universally true moral claims are describing. Which then leaves the question of how to tell which moral claims are true or false... but you've already got hedonism for that. It'll just have to be an altruistic hedonism, like utilitarianism, since universalism precludes egoism.
(But if you then apply the analogue of critical rationalist epistemology to that process of sorting out what's good in an altruistic hedoistic sense, you end up precluding consequentialism, as the moral analogue of confirmationism, leaving you with a kind of liberal deontology instead of straightforward utilitarianism).
values are both objective and subjective — Pinprick
Perhaps objective as in universal (i.e. altruistic), but not objective as in transcendent; and subjective as in phenomenal (e.g. hedonistic), but not subjective as in relative?
