To help focus the issue, consider first a clear case of a sentence-token’s being a priori, but not a priori knowable in the above senses. Suppose that Leverrier writes in his diary
(N) “Neptune is the planet, if any, that perturbs the orbit of Uranus”.
Let us suppose further that Leverrier has introduced “Neptune” into his idiolect as a name for whichever planet, if any, perturbs the orbit of Uranus. Given this, the thought expressed by N is both a priori and has a necessary epistemic intension (since it expresses the thought that the planet, if any, that perturbs the orbit of Uranus is the planet, if any, that perturbs the orbit from Uranus).
However, Dowell continues, anyone reading the diary has no way to know a priori, i.e. without experiential justification, what thought (N) expresses. (Indeed, she doesn't say it, but presumably we cannot even know what language it's written in. For all anyone knows a priori, the squiggles might have landed on the page through a massive coincidence of spilt ink, and so not mean anything at all.) So although (N) is a priori in Chalmers' thought-derived sense, the sentence itself is not a priori knowable. Someone presented with the sentence could not determine a priori whether it was true; first they would need to know what it means.
Dowell then argues:
[I]t is unclear how the a priority of sentence-tokens in Chalmers’ sense is a rational notion at all, given that it is divorced from what is a priori knowable and not characterized in terms of rational accessibility to agents, even idealized ones.
But this is silly -- Dowell is asking the impossible. On (my understanding of) her characterization of what it would take to know a sentence a priori, there are no a priori knowable sentences. So Chalmers' conception of sentence apriority is divorced from ["what is a priori knowable", namely:] nothing at all!
The core issue here concerns what sort of link we could hope to establish between reason and meaning. Dowell begins with the question of whether the 2-D framework can "ground an a priori-accessible, extension-fixing component of content for very many of our terms and sentences." But to ask that reason alone tell us the meaning of squiggles is certainly too demanding. It would be ludicrous to hold that sentence apriority is a matter of being able, when presented with some squiggles, to determine by reason alone whether the claim made by the squiggles is true.
No, we should be satisfied to make more modest demands on reason. A more reasonable challenge is to ask whether there is a component of content that is constitutively tied to apriority in the sense that Chalmers describes. Dowell complains that "this interpretation presupposes rather than grounds an a priori available component of content." But that only seems an objection if we misunderstand the aim of the framework. If what it takes for a component of content to be "a priori available" is for an agent to be able to determine the content of squiggles by reason alone, then (obviously!) no-one can provide such a thing, and nobody is trying to.
It might help here to invoke the distinction between semantics and meta-semantics. Whereas first-order semantics concerns the meaning of expressions, meta-semantics asks about how words get assigned their meanings to begin with (cf. the problem of intentionality). Now, Dowell is effectively demanding an a priori method for answering metasemantic questions (e.g. does some token of 'tiger' mean to talk about big cats or sofas?). But that's a ridiculous demand. We can all agree that such meta-semantic determination is an empirical matter. (Dowell calls this "the incontrovertible point".)
No, the only reasonable question to ask here is the first-order semantical one. Given that the words 'tiger' and 'sofa' actually have such-and-such semantic content (in particular, their respective primary intensions), can we determine whether "tigers are sofas" is a priori false, just in virtue of the meaning of the terms? Plausibly, we can. Perhaps a tiger carcass could be used in sofa manufacture, but I can't imagine any scenario in which it would turn out that tigers just are sofas. (Again, don't confuse this with the meta-semantic issue of whether we can imagine scenarios where the word 'tiger' would turn out to mean something completely different.)
Another way to put the point is to insist that our idealized agent be granted full command of the language in question. Perhaps Dowell intended to allow agents a coarse-grained version of the language, such as that which is shared by all competent English speakers. That would suffice to allow us to identify sentences like "Hesperus is Hesperus" as a priori, but not speaker-relative apriorities such as that expressed by (N). The problem with this is that it excludes a key component of meaning (according to the 2-D framework), namely, the 1-intension. Chalmers is explicit that 1-intensions are speaker-relative (hence the need to speak of sentence tokens rather than types), so the appropriate "language" will need to be fine-grained enough to accommodate this. In other words, the agent needs to be given the idiolect of the speaker.
Then the relevant question becomes whether an idealized agent who reads (N) in Leverrier's idiolect could, through a priori reasoning alone, come to know that (N) is true. And the answer is surely 'yes'. A perfectly competent speaker of Leverrier's idiolect will grasp the primary intension of 'Neptune' so used, and thus recognize the thought expressed by (N) as being 1-necessary and hence knowable a priori. This seems to be "an interpretation that genuinely links reason [and] meaning... in a substantive way." Of course if we strip a sentence of its meaning, then our rational notions can get no grip on it. But that does nothing to cast doubt on Chalmers' links between meaning, reason, and modality. The claim isn't that reason can magically discern the meaning of squiggles. Rather, it is that reason can determine whether, given the meaning of a sentence, it must be true. This establishes substantive connections between the semantic notion of a primary intension, the rational notion of apriority, and the modal notion of 1-necessity.