Interestingly both Peirce and James (the pragmatists I've read any of) initially explain reality as correspondence. For instance, Peirce says "Thus we may define the real as that whose characters are independent of what anybody may think them to be" ("How to Make Our Ideas Clear"). He then of course later goes on to say that what this really means is that reality is "the opinion which is fated to be ultimately agreed to by all who investigate". (Investigate here being scientific investigation.) Similarly, James initially agrees to this characterization "Truth, as any dictionary will tell you ... means [our ideas] 'agreement', as falsity means their disagreement with 'reality'." ("Pragmatism's Conception of Truth") James conception of what this means is less idealistic than Peirce, concluding, "True ideas are those that we can assimilate, validate, corroborate and verify. False ideas are those that we can not.".

In these two cases, the Pragmatists conception of reality is based on their views of meaning. More sophisticated modern quasi-Pragmatists like Putnam or Goodman will come to similar conclusions instead based on a sort of conceptual relativism. To quote Putnam "A sign ... can correspond to particular objects within the conceptual scheme of users [of those signs]. 'Objects' do not exist external to those conceptual schemes." ("Two Philosophical Perspectives"). Goodman's Ways of Worldmaking is based on similar ideas and is also well worth a read.

To connect this background to your post, it seems it might help to construct a more adequate reply to the critic. I assume you are thinking of the following sort of criticism:

Here is a claim that is true or false (a) There are infinitely many binary stars. For simplicity, assume (a) is true. But pragmatists seem to have no way of accounting for the truth of (a). After all (a) is not verifiable one way or another (even after the end of inquiry) and so by pragmatists lights cannot be true or false. (This is a criticism that Alston raises against Putnam in "A Realist Conception of Truth".)

The reason I find your reply to be lacking is that it seems to beat a quick retreat into skepticism. But you are a pragmatist not a skeptic! Surely by any good pragmatist lights ready-to-hand claims like "There is a keyboard right here", "I am typing", etc. are true. The retreat to skepticism ("we have no right to ever assume something is real") is actually contra-pragmatism, because it assumes there is a sensible non-pragmatist reading of the word 'real'. This seems to be where you are going with "The most useful idea we have, and indeed the most pragmatic, is the concept of mind independent reality." However, I don't find the idea of utility the most compelling way to put Pragmatism. Sure Pragmatists like James will write off a lot of discourse as "useless" or meaningless (take James' squirell example). But the utility James is worried about (and it seems any pragmatist should be worried about) is the difference it makes to experience. (Here is where pragmatism and empiricism come together.)

So a hard lined Jamesian line would be that the putative counterexamples the critic poses, like "there are infinitely many binary stars", are meaningless. I don't find this a particularly compelling response, as (a) is perfectly meaningful. A better response then, it seems, is the one Putnam offers (the introduction to Realism with a Human Face), in which (a) is meaningful because it is part of our conceptual scheme. This it strikes me is still something of a pragmatist (because it keeps a narrow focus on the experiences and sense-making abilities of actual people), empiricist (because our standard for truth is still ideal justifiability) but also less crazy than the traditional pragmatist line.

In conclusion, I find old school pragmatism and 'utility'-talk less convincing than more modern flavors and in particular giving a worse reply to the kind of criticism you are trying to respond to.