Thanks for the analysis!
Here's my spin on it, rooted partly in my background in the music of the eastern Mediterranean and SE Europe.
The notion of a "mode" is different than the notion of a "scale". A "scale" tells you which notes to play. A "mode", in addition to this, also gives you guidelines for forming melodies using those notes. Being the technical person that I am, I think of it a bit like the mathematical notions of a scalar vs. a vector: A "mode" also gives you a direction.
That is the difference between the Ionian and Hypoionian modes: They have the same scale, but one of them resolves to the 4th note instead of the 1st note (the "tonic").
And really, even our friend the "major scale" is really a mode, or, we use it as a mode: It resolves to the tonic, and uses the 5th note (the "dominant") as a sort of frequent layover; the 1st and 5th notes together anchor the melody.
(There are modes in the world where that other anchor note, that layover note, is not the 5th. I don't know enough about Western modes to know if any of them do that.)
Now: That other anchor - the dominant - splits the mode into 2 pieces. Let's take a C major scale:
C D E F G a b c
The 5-note bottom component of the mode, from the tonic to the dominant, is:
C D E F G
The 4-note top component of the mode, from the dominant to the next tonic, is:
G a b c
The bottom part is a major group - it comprises the beginning of a major scale.
The top part is also a major group - it's sort of like the beginning of its own major scale, starting on G.
So: A major scale consists of a major group on the bottom + a major group on top.
A myxolydian scale consists of a major group on the bottom + a minor group on top.
A Dorian scale consists of a minor group on the bottom + a minor group on top.
As for the minor scale (I assume you mean natural) - it has a minor group on the bottom, and a top group that has its own distinct sound - Phrygian.
So, the four mainstream modes are composed of 3 types of groups:
* Major group: Has a sharp, happy sounding 3rd. Examples:
- D E F# G A
- G A B C
* Minor group: Has a flat, sentimental or mystical sounding 3rd. Examples:
D E F G A
G A Bb C
* Phrygian group: Has that distinct drooping sort of sound, with the flat 3rd as well as flat 2nd. Examples:
D Eb F G A
G Ab Bb C
* Identify the two anchor notes: The tonic and the dominant.
* Identify the types of the two groups comprising the scale - the 5-note group from the tonic to the dominant and the 4-note group from the dominant to the next tonic.
There - you have your mode (well, technically, scale).
If you feel a compulsion to assign a name to the mode:
[ major -- major ] = major
[ major -- minor ] = Myxolydian
[ minor -- minor ] = Dorian
[ minor -- Phrygian ] = minor