D is the bottom note on pipes, whistles and (mostly) flutes, which is why the majority of tunes don’t go any lower.
But there are plenty of good fiddle tunes that do, going right down to G (lowest note available on a fiddle). Pipers, fluters and whistlers have to fake these notes (play them an octave up, play something else that fits), but box players don’t - be happy!
Classic tunes that go down low: Farewell to Ireland, Lads of Laois, Sean Ryan’s jig - there are hundreds more.
Mind you on the box, those lower notes will get you tearing your hair out in the early stages, because the notes below D get “out of synch” - for example, on your C#/D box your low B is on a button nearer your chin than your low A.
As for the three repeated As - yes they can sound boring. The easiest way to tackle them is to stick a cut (grace note) in between the second and third of them. (This is what you seem to have found, except it would be more usual to grace with a higher note rather than a lower one.)
E.g. play FAA {d}ADD. The high d in the braces is your cut - clip the button above the A immediately before you sound the third A. This is exactly what you might do on a whistle or flute, btw.
Another neat grace you can use on a halfstep box like a C#/D or B/C is to use the note a semitone below your main note, from the outer row. For example you can grace an A with a quick (very quick!) G#. Without trying it, I’m not sure what it will sound like in this passage, but it’s a great trick to keep up your sleeve, giving a very characteristically Irish-box sound. It’s the nearest thing you can get to a slide up to a note.
Going back to repeated notes, in the early stages it’s hard to make repeated notes like this sound not-lame, but as your control over your fingers (and bellows pressure) improves, you’ll find you can make them much smoother.
Until you get to that point, another way to get them sounding smoother, more legato, is to use different fingers. Try playing FAA ADD with fingers 121 211… it’s a trick I use a lot. I wrote a topic about it a while back, here it is: http://chiffboard.mati.ca/viewtopic.php?t=40219
Cheers
Steve