Theorists differ on the precise usage of "diatonic" when it comes to minor. There isn't any substantial disagreement on the behavior of minor-key common practice music, just in the best use of terminology. Under the most expansive interpretation of the word, any notes of the minor scale, including both versions of the sixth and seventh scale degrees, are diatonic, and thus, at least technically, any chords using those notes would be diatonic. This is the same as saying that all the chords in the natural, harmonic and melodic minor scales are part of the key—however, I would prefer to step back from the idea that those scales are specific entities in common-practice music. Until the 20th and 21st centuries there was no such thing as a piece in "A harmonic minor" or "A melodic minor"; there was just "A minor" which has variable sixth and seventh scale degrees depending on musical context.
The most restricted use of "diatonic" holds that only the most common progressive (not sequential or passing) harmonies should fall under the term. By far, the most common functional harmonies in a minor are:
amin bdim C dmin E F g#dim
i ii° III iv V VI vii°
That is to say, the chords of the "natural" minor scale except with a raised leading tone for V (E) and vii (G#).
I don't care much about how we use the diatonic term, as long as we're clear that these are the most important harmonies for functional harmony in minor.
The only other harmonies that the most expansive definition of diatonic would add to the list all involve the sixth or seventh scale degrees of course, and their prominence varies substantially. The V and vii without the raised leading tone aren't that uncommon, but they are vastly more significant in sequences (e.g. i – iv – bVII - III …) and in passing harmonies (e.g. i – v6 – VI). The sequence example is the beginning of a minor-key circle-of-fifths sequence with the major VII built on the unraised seventh scale degree, and the passing example is a minor v in first inversion (unraised leading tone) to pass between i and VI. Meanwhile, unlike V and vii, III almost always has the unraised leading tone, and is quite rare as an augmented harmony III+.
All of the standard harmonies that include the sixth scale degree use the unraised version, and the versions with raised 6 are relatively rare. Probably the most common is IV, which is sometimes necessary to create smoother voice leading to V (in other words, to eliminate the augmented second between the lowered sixth scale degree of iv and the raised seventh scale degree of V). It's less common to do this with ii (turning a diminished triad into a minor triad), but not unheard of. Raising the sixth scale degree of a VI chord in minor turns it into a diminished harmony (often written in Roman numerals as #vi°) that is used as a passing chord leading up to vii° or V6. Again, that is used to eliminate what would otherwise be an augmented second in the bass line.
So, yes, I think your final list is a good list of the standard diatonic harmonies in a minor as long as you get rid of e minor and G major. Those two harmonies mostly happen in sequential or voice-leading circumstances. I think it's probably most useful however to acknowledge that the less common versions of all of the sixth- and seventh-scale-degree-having harmonies aren't chromatic (and hence are indeed diatonic), they're just less common and/or used for other contexts.