Unlike Attic, there is no single, consistent “Doric” dialect on which a systematic grammar could be based.
On the one hand, there are local (“epichoric”) Doric dialects reflected in inscriptions from Doric-speaking areas, mostly the Peloponnese, which are very different from one another and in most cases quite different from “Doric” literary texts. On the other hand there are literary texts that to a greater or lesser extent exhibit certain Doric features, but the Doric literary texts are not consistent with one another, either.
Moreover, the corpus of surviving Doric literary texts is much, much less extensive that the Attic corpus, and consists entirely of poetry. No corpus of literary Doric prose has survived (though I think there may be a handful of fragments). So there’s really not a large enough body of Doric writing on which a useful and systematic grammar could be based.
The most salient and recognizable “Doric” feature is of course the retention of inherited long alpha instead of Attic-Ionic eta, but this is a feature of all dialects other than Attic-Ionic.
Early on, Doric became associated with choral poetry, or rather choral song, and it was obligatory for choral poetry to be composed in some form of Doric. The language of the choral poets Alcman, Steisichorus, Pindar and Bacchylides is to a greater or lesser extent Doric, even though Pindar, for example, was a Boeotian from Thebes, whose native dialect would have been some sort of “Aeolic”. Likewise, as a result of the convention that choral poetry much be composed in some sort of Doric, the choral songs in Athenian drama are Doric-colored, but really they are composed in something like Attic, or rather a common Greek literary language, with some recognizably Doric features superficially imposed.
The difficulties of identifying a single Doric dialect on which to base a Doric grammar are compounded by the fact that the supposedly Doric literary texts that have survived have come down to us in a form based on editions prepared by Hellenistic scholars several centuries after the texts were originally composed (after cir. 300 BCE). These scholars are believed to have sometimes substituted what they thought were Doric forms (“hyper-Doricisms”) for the words they found in the texts on which they based their editions–for example, erroneously substituting long alpha for original eta that occurred in all Greek dialects. So we can’t always be sure that supposedly Doric forms in literary texts are genuine. And on top of that, there are spelling issues such as those you identified, which may or may not be the result of Hellenistic editing.
The good news is that Doric forms appearing in literary texts are not all that extensive and not too hard to identify with a little experience, and apart from long alpha, most commentaries will identify and explain the Doric forms for you. Once you’ve engaged with a few Doric literary texts, you will become adept at recognizing the non-Attic forms.