"the vast majority of those Mixolydian tune book songs are not Mixolydian modal songs. They are Ionian Mode songs being played in Mixolydian DAd using the 6+ fret."
This is correct - or you could play across the strings and use the 2nd fret of the middle string.
This shows the confusion created by calling tunings by mode/scale names. Think of the modes as scales and scale variations. Ionian mode is a fancy name for the major scale, the old do re mi... Myxolydian is a fancy name for the major scale with the 7th note flatted. (Aeolian and Dorian are fancy names for two kinds of minor scales.)
On most modern dulcimers (w a 6.5 fret):
When tuned DAD you play an ionian/major scale from 0 (open) to the 7th fret using the 6.5 fret and skipping the 6th fret.
When tuned DAD you play a myxolydian/flat-7 scale from 0 to 7th fret using the 6th fret and skipping the 6.5 fret.
DAD tuning was called "myxolydian" because on the original dulcimers - with NO 6.5 fret - it is the only scale you could get going from open to the 7th. Also, that's how you MUST tune the dulcimer to play a song like Old Joe Clark that uses a flat 7th (on 'Clark': 4 - 5 - 6 - 5 - 4 - 3 - 2...)
To play an ionian/major scale on a trad dulcimer - with no extra frets - you MUST tune to DAA, and the scale starts with the D that's now at the 3rd fret, and you play 3 - 10 on the frets. If you tune DAA on a modern dulcimer, you still play 3 - 10 for the major scale, but you have to make sure to skip the 6.5.
That's why DAA tuning became called "Ionian" - b/c that's the way you have to tune to get a major/ionian scale on a traditionally fretted dulcimer.
With the 6.5 fret (or playing across the strings) you can find the pure major scale songs even if you're in DAD tuning.
Bottom line: It's NOT really the tuning that is "myxolydian" - it's that that tuning allows you to play the myxolydian scale, in particular on a dulcimer with no extra frets. Same with all the other Greek names.
I tend to stay in DAD because I can play either mode with no retuning. However, you can't play a D-myxolydian scale on a dulcimer tuned DAA - unless you use the bass string.
I think of the DAD tuning as 'containing' the DAA within it - on that middle, A, string - but not vice versa.
Hope that makes sense. It can be a little confusing!