It's not a strawman at all, though the critique does adopt a kind of casually irreverent style while making its substantive points.
My charge is that you did not refine our understanding of what is "objective" but instead discarded the term entirely, and that this is an even worse way to model reality than using the overly-idealized notion of what makes something objective.
Here's an example of the linguistic tomfoolery in action: 'to say that “Astronauts walked on the moon” is true is to presuppose the validity of all the struggles and biases involved in generating NASA’s maps and models of nature'
There's no pragmatism here, only implications of invalidity and a misassignment of credit for reliable knowledge and a confusion about the distinction between enacting and observing. Pragmatic is to say: "Astronauts walked on the moon" is objectively true because we have tons of objective evidence that it happened.
If you want to investigate the relationship between linguistics and epistemology (and probably ontology because how can you escape it?) when it comes to the moon landings, you simply can't add value with statements of this simplicity.
Simply "I exist" is equally fraught as a statement and is a much better example than bringing in all the potential confusions about NASA. To say "I exist" is true presupposes the validity of our notions of identity and the linguistic expression of this identity, and of the distinction between existence and non-existence and the linguistic expression thereof. There's a reason that Tarski chose "Snow is white" as the exemplar for developing notions of truth about the physical world, not "Sir Francis Drake circumnavigated the globe." You imply that your point is about issues that might be of some doubt, but your point applies equally well to the very most mundane and obvious statements that people ever make. You are not properly developing intuitions about your perspective.
Any epistemology that fails to account for the extraordinary agreement in detail and in consequences of utterances like "a burning candle is hot" is a poor theory indeed. And once you account for this extraordinary reliability, there is no problem with using our perfectly good word to describe this state of affairs: "objectively, a burning candle is hot". Once you start getting into the ontology of hotness and the neuroscience of sensation, it's easy to get confused about the extraordinary underlying reliability that we were trying to account for in the first place.
And whether we account for this difficulty using a foundationalist framework with sketchy foundations, or a coherentist framework with every workable model known sharing identically the same large subset, or something else, we do not in practice end up all inhabiting our own mutually incomprehensible realities. A burning candle is hot.
Fundamentally, "a burning candle is hot" is qualitatively (or so quantitatively that it is effectively qualitatively) different from "the best desserts contain chocolate". If we want to take a pragmatic science-like view of things, recognizing that the tower of ontological justifications needed to completely support our epistemology is compromised by our lack of complete understanding (and, as far as we can tell, always will be to a critical extent).
So that is the thrust my criticism. You took a perfectly good word and threw it away on the basis of poorly-framed criticism. Hence my jibe about not trusting philosophers with words.
If you're doing pragmatism--really, seriously, wholeheartedly--you will avoid casting unfair doubt on things like moon landings as opposed to your personal existence; and you will recognize that pragmatically, "objective" is a useful and well-defined characteristic of certain types of statement that we should keep using (while recognizing that, like most things, it has some rough edges that we need to beware of in tricky cases).
I'm totally cool with pointing out the rough edges, but not with implying that it's all edges, nor with throwing away useful concepts because of rough edges.