Travis, I play fairly often in a multi-instrument jam and move very easily among the keys of C, D, G, and A, as well as their relative minors of Am, Bm, Em, and F#m.
I tune CGc to get the keys of C and Am. The rest I get out of a DAd tuning with the use of a capo. The capo at the third fret gives you G and Em and the fret at the fourth fret gives you A and F#m.
The advantage to this is that you are playing in a 1-5-8 tuning the whole time, so everything you have learned in that tuning can be used in any of those keys, and your playing can be more versatile than limiting yourself to chords, as you would have to do if you stayed in DAd and used a lot of barre chords.
And by this same system you could get the key of F (or Dm) by tuning CGc and putting the capo at the third fret. So that gives you 10 keys already without having to carry around more than one dulcimer.
updated by @dusty: 07/08/15 09:40:38PM