Salut, and welcome,
Your instincts are good--the chords you're trying don't sound "right" to you, because this is not how accordion bass harmony is done in traditional Irish accordion. (Here I am talking about "traditional" Irish accordion. If you don't care about sounding traditional, you can of course please yourself and do whatever works for you---jazz inversions, 12-tone serialism, the sky's the limit!)
Irish tunes are largely modal music. Modal scales pre-date Western music's major and minor scales. You could say modal scales are "both" major and minor. Or you could say they are "neither." Due to this, the pre-set chordal buttons on Piano accordions or chromatic B or C system accordions often don't "sound right" with Irish tunes. This is the case even for tunes that do fit a largely major mode such as "Moving Clouds."
The accordion seen as the most traditional in Irish music is the bisonoric or diatonic button accordion--these instruments have only single-note basses and a major chord. These boxes often come with a slider or switch enabling the player to remove the third from the chord. The reason for this is not only that those boxes are too small to allow more chords. It is also because dominant seventh, diminished, augmented, and jazz chords do not "fit" or "sound right" if you are playing traditionally. This is to a large degree derived from the drones and chords used by the Irish pipers. They do not play dominant seventh, diminished, or augmented chords.
Unisonoric accordions like piano or chromatic button accordion can be fantastic for Irish music. But in the same vein as the pipers and the diatonic box players, players of piano accordions or chromatic accordions who wish to fit the traditional Irish style, use their single-note bass buttons a lot. They use single-note drones, or combine two single notes for what fiddlers call a "double stop"--an octave or a fifth. They stay away from the chordal buttons with the exception of using the major chord in the instances when it fits. When it doesn't fit, one might use a single bass note or a "double stop" made up of a root note and its fifth. Again--you can do other chords. But that oompah stradella sound is not really the traditional Irish sound.
Often in Irish traditional music a box player does not play chords or basses at all. The rule of thumb is to go light or even go silent if there is already a rhythm instrument present. Here is a recording of traditional Irish piano accordion playing tunes which include "Moving Clouds." Basses are not absent because these lads can't play. They are virtuosos. You don't hear basses because it is considered intrusive in the Irish traditional style:
Of course, players do use basses at times, particularly at a big dance. Here is a piano accordion player doing "Moving Clouds" with some basses and chords. But I believe the only chord you hear in this instance is the major chord, and he's using it only when it fits. The rest of the time it's just a quiet single-note bass here and there, or perhaps a double-stop made up of a tonic and fifth single note buttons.
Here is the brilliant Scottish piano accordion player Phil Cunningham doing "Moving Clouds." No accordion bass audible. Because there is already drums and piano there. Note the piano accompaniment is backgrounded, not foregrounded, and you are not hearing seventh, diminished, augmented, or jazz chords from the piano. That is how you want to do you accordion basses if you do them--quiet, backgrounded, and simple:
Both chords will lead the ear to the G chord. The D7 will lead the ear with a bit more urgency though.
