First it fails, because pretty much everything Kant wrote about geometry runs into the serious problem that his whole idea is deeply connected to Euclidean geometry being the one, true correct geometry.

That's true, but it doesn't sound relevant to the subject of the article.

Second, this runs into the earlier discussed problem of trying to discuss what major philosophers meant, as if that had intrinsic interest.

A solid blow.

Third, a glance strongly suggests that they are ignoring the large body of actual developmental psych data about how children actually do and do not demonstrate intuitions for their surrounding geometry.

That might be relevant to Strawson's view, I'm not actually sure what he says, but it's not relevant to Kant's view. 'A priori' does not mean 'innate' or biologically determined.