Isn’t a law of logic defined by its origin rather than by how general it is? In other words, a law of logic comes from Reason itself, not like a law that describes the behavior of physical things (a law of nature).

If that’s right, then there’s nothing in the concept of a law of logic that demands it must always apply universally. That just seems to be a characteristic these laws often exhibit, but it’s not essential to what they are. So, if it turns out that all proposed logical laws have exceptions, it doesn’t mean there are no laws of logic—only that they are more specific than we once thought.

Well to be clear, I don't think:

Which is not surprising, as the Logic Of All And Only Universal Principles would need to have its laws apply in complete generality, and thus talk about every other logical apparatus in existence.

this is what she is doing. To do this would be to ignore what the most popular pluralists (B&R) and what most monists say about their own positions. As fdrake says, if one is allowed to appeal to "every other logical apparatus in existence," and its self-defined capacity to produce valid inferences, then it is very easy to come up with "knock down arguments" demonstrating nihilism. But Russell is willing to admit that nihilism is a slim minority opinion that is often considered "absurd," which would be strange indeed if it was a position that is easily demonstrable. Hence the argument focuses on the plausibility and popularity of counterexamples, not their mere existence.

I don't really know what else to say here, SEP, IEP, the books I've referenced, and similar resources point out that this is not how the debate is defined; there is wide agreement that people have created logical systems that alternatively dispense with all of the "laws of logic" (or more accurately, would render the logical consequence relationship empty).

I feel like part of the confusion here is that this question is one of what holds for valid inference (true premises ensure a true conclusion) as a whole, across all logics, which in turn means that the common way of thinking of validity in a purely internal sense essentially begs the question here. (Russell doesn't do this BTW, although it seems this could have been made clear. Her intro on logical nihilism is clearer.)

Logical Monism holds that there is only one correct or true logic, meaning that a single set of logical rules or principles governs valid reasoning universally. Proponents believe that this one logic captures the essence of valid inference across all contexts. [Note, books making the case for monism I have seen generally focus on applied logic as the target for their argument. The analogy here would be the difference between trying to identify the physical geometry of the world versus the purely mathematical consideration of very many geometries.]

Logical Pluralism asserts that more than one logic can be correct, depending on the context or purpose. Different logical systems may be valid for different kinds of reasoning (e.g., classical logic for everyday reasoning, but other logics like intuitionistic or relevance logic in specialized cases). [The most common historical example here I can think of is the claim, arguably in Aristotle, that the Law of the Excluded Middle does not apply to statements about the future].

Logical Nihilism denies that there is any objective or true logic at all. It suggests that no logical system accurately captures reasoning or inference, and that the concept of "correct" logic may be meaningless or arbitrary. [Or, one way to put this more specifically, as Russell points out in a footnote, is idea that the logical consequence relationship in natural language (and so arguably scientific discourse as well) is actually empty. Of course, the nihilist may also recommended other ways to retrieve the concept of a "correct logic" as well.]

Part of the confusion is that just how one wants to define these might vary quite a bit, although they are generally not going to be defined in terms of "every logical apparatus in existence," since I think everyone is going to agree here making the debate a bit trivial.