Thanks for this. Here's Stanford Encyclopedia of Philosophy's first paragraph:

"Pragmatism is a philosophical tradition that – very broadly – understands knowing the world as inseparable from agency within it. This general idea has attracted a remarkably rich and at times contrary range of interpretations, including: that all philosophical concepts should be tested via scientific experimentation, that a claim is true if and only if it is useful (relatedly: if a philosophical theory does not contribute directly to social progress then it is not worth much), that experience consists in transacting with rather than representing nature, that articulate language rests on a deep bed of shared human practices that can never be fully ‘made explicit’." https://plato.stanford.edu/entries/pragmatism

I'd say pragmatism is as much a criticism of certain directions in philosophy as anything. It's a method of asking of philosophical distinctions "what difference would that make." But instead of turning toward skepticism it seeks to reorient philosophy and reasoning toward the fulfillment of human goals.

There are also like 3 different ways 2+2!=4.

Outer universe with different math - We're a simulation inside a different universe that runs on different math where 2+2!=4, but the math inside our universe is consistent. This is the same as 2+2=4 for most purposes. This is imaginable, I think...

Active demon - there's a demon that controls all your inputs, in a way that's inconsistent with any reasonable mathematics, but you can't tell. This is the least likely, and if it were true I wouldn't even consider myself a person.

Math is flawed - the whole concept of arithmetic, or all of mathematics, is inconsistent and it's impossible to construct a system where you can actually prove 2+2=4. This doesn't necessarily mean two apples and two apples makes four apples - it just means the apples behave like they do for other reasons than arithmetic. This is conceivable.

I like your description here a lot. I am no expert but I agree with your characterization that Peirce's pragmatic maxim offers something really valuable even for those committed to correspondence and, more generally, to analytic philosophy. 

On Rorty, his last book was just published posthumously and it offers an intriguing and somewhat different take on his thinking. The basics haven't changed, but he frames his version of pragmatism in terms of the Enlightenment and anti-authoritarianism. I won't try to summarize; your mileage might vary but I've found it interesting. 

For me, again not as any kind of philosophy expert, the original appeal came from disillusionment with metaphysics. It seemed to me as a student that the arguments were just language games. The pieces might be really logical in relation to each other but they had no force because there was no solid foundation. There was always an assumption that could be challenged. (It's admittedly hard for me now to describe this without slipping into Rorty-esque language.) 

And then I read Rorty's Philosophy and Social Hope which was my introduction to pragmatism, and which seemed to directly address these concerns. Putting goals up front seemed a way around the constant possibility for objections: at some point we all have things we want to achieve and that can be the starting point for something. (Rorty also sort of gives you permission to stop reading philosophy and get on with it which at the time I appreciated.)

I imagine most EAs would not really enjoy Rorty because he sort of delights in constantly knocking seemingly common-sense notions of truth and a lot of his best writing is purposefully loose and interpretive. (Side note: the new Rorty book has some interesting nods toward causality; he's still rejecting correspondence but recognizing that causal forces limit our actions. One more reason I read him as attacking philosophy more than attacking reality.) Still, I think he offers a starting point that can really work for building up an epistemology based on application and moral goals rather than on metaphysics. And that's the part I think EAs might find exciting and interesting.