Dennis, You can play in DAA using DAA tabbing with people who are playing DAd with DAd tabbing with one condition. The tune in DAd must not be in the true Mixolydian mode with a flatted seventh note. An example of this type of song is Old Joe Clark it needs that flatted note. If, however, you have a dulcimer with a 8+ fret and are in DAA, you can go ahead and play it. When playing in DAd most people are really using a note pattern that also fits in DAA, but they have done a subtract 3 on the DAA tab to get DAd. Here's Brother John in DAA:
3453,3453, 567,567,787653,787653,303,303 In Dad you deduct 3 and end up with
0120, 0120, 234,234,454320,454320, 0 0middle 0, 0 0middle 0. Since the D is at 0 in DAd and at 3 in DAA you are playing the same notes in either tuning.
So if you are handed tab in DAd but are tuned DAA, whip out a pencil and add 3 to your melody line, you'll be done in a minute and be ready to play the melody. Just remember that 6+ becomes 9. You'd need a 8+ if you had a tune tabbed DAd using a 6. Figuring out chords will come later.
Having a 6+ can come in handy even in with a tune that normally would fit into Ionian. I have a version of an old Scottish folk tune that call for a flatted B in the key of E. It goes from the natural B to a flatted B to a natural B all in the same measure. So it frets 7/6+/7. If I tried to tab it in DAd, I'd have 4/3+/4. I don't have a 3+ on my fret boards.
As for using other tunings, DAC is the Aeolian minor tuning and will sound very strange if you try playing DAD tab when tuned that way. DGD is a reverse Ionian in G not in D. You have a D drone and a G drone and play the melody on the D string starting at 3 which would be the G. GDD is the more traditional way of playing G Ionian, but it's easier to go from DAd down one note on the middle to G to get a quick key change. So you can't really use DAD tab and stay in the key of D using those two tunings and still play with DAd players.