Benacerraf convinced me that either mathematical sentences have different logical forms than non-mathematical sentences or that mathematical knowledge has a different form than non-mathematical knowledge. It sounds like your view is that mathematical sentences have different forms (they all have an implicit "within some mathematical system that is relevant, it is provable that..." before them), and also that mathematical knowledge is different (not real knowledge, just exists in a system). In other words, it sounds like you just think that epistemic uniformity and semantic uniformity are not important features of a theory of mathematical truth. That comes down to personal aesthetics and meta-beliefs about how theories should look, so I will just talk about what I think you're saying in this comment.

I think what you're trying to say is that mathematical statements are not true or false in an absolute sense, only true and false within a proof system. and their truth or falsehood is based entirely on whether they can be derived from within that system. 

If that's true, math is just a map, and maps are neither true nor false. If math is just a map, then there is no such thing as objective mathematical truth. So it sounds like you agree that knowledge about any mathematical object is impossible. But when you say that "Epistemic uniformity simply states that math is a useful model", I think that's a little different than what I intended it to mean. Epistemic uniformity says that evaluating the truth-value of a mathematical statement should be a similar process evaluating the truth-value of any other statement.

The issue here is that our non-mathematical statements aren't only internally true or false, they are actually true or false. If you asked someone to justify sentence (1), and they handed you a proof about New York and London, consistent on a set of city-axioms, you would probably be pretty confused. Epistemic uniformity says that a theory of mathematical truth should look relatively like the rest of our theories of truth - why should math be special?

I'm going to take a slight objection to using the phrase "discoverable experimentally" to describe proving a theorem and thinking up numbers, but let's talk about those examples. To me, it sounds like that is doing work within a system of math to determine whether a claim is consistent with axioms. There is some tension here between saying that math is just a tool and thinking that you can do experiments on it to discover facts about the world. No! It will tell us about the tool we are experimenting with. Doing math (under the intutionist paradigm) tells us whether something is provable within a mathematical system, but it has no bearing on whether it is true outside of our minds.

(Side note about intuitionism: 

I think it's important to prevent talking past each other by checking definitions, so I'd like to clarify what you mean by intuitionism. In the definition I'm aware of, intuitionism says roughly that math exists entirely in minds, and the corresponding account of mathematical truth is that a statement is true if someone has a mental construction proving it to be true. Please let me know if this is not what you meant!

My main objection with intuitionism is that it makes a lot of math time-dependent (e.x. 2+2 didn't equal 4 until someone proved it for the first time). Under an intuitionist account of mathematical truth, you can make sentence (2) true by finding three examples that fit. But then that statement's truthhood or falsehood is independent of whether the mathematical fact is really true or false (intuitionists usually don't think there exist universal mathematical truth). It seems to me that math is a real thing in the universe, it was real because humans comprehended it, and it will remain real after humans are gone. That view is incompatible with intuitionism.)

(Another note - can you be a bit more specific about the contradition you think is avoided by giving up Platonism? I think that you still don't have epistemic and semantic uniformity with an intuitionist/combinatorial theory of math)

This is definitely not a "big problem" in that we can use math regardless of what the outcome is. 

It sounds like you're arguing that semantic uniformity doesn't matter, because we can change what "exists" means. But once you change what "exists" means, you will likely run into epistemological issues. If your mathematical objects aren't physical entities capable of interacting with the world, how can you have knowledge that is causally related to those entities? That's the dilemma of the argument above - it seems possible to get semantic uniformity at the expense of epistemological uniformity, or vice versa, but having both together is difficult.

To provide a more concrete example, I would say that the claim "There are at least three Jedi older than Anakin Skywalker" is, in the interpretation of the sentence almost anyone who understands it would use, a true statement, even though Jedi certainly do not exist in the same sense that New York City exists. I would not say that the fact that Jedi and New York exist in very different ways really violates Semantic Uniformity in any substantial way.