I have always been a fan of Gary Ewer’s online resources for learning basic music theory and improving your songwriting skills, but when the subject is very close to my heart, like Modal Chord Progressions, all of my lights and buzzers start to go off simultaneously!!
Gary Ewer has a post about how to get Lydian Mode progressions to work. I’ve tried some of these ideas over the years with limited success, but Gary goes into some detail about the specific problems with the Lydian, and how your ear can get easily led to the relative major (Ionian) or other relative mode.
If you want to try Lydian Chord Progressions on your DAD-tuned dulcimer, I suggest G Lydian as your tonal center. This way, you might have a home G chord, going to an A chord, then to something other than D. Why don’t you want to go to D? Because it will sound like a progression that comes HOME to D!! (IV – V – I)
What you really need to do is get the G chord to sound like HOME: even if it has that unsettling #4 (C# which you can find on the 2nd fret of the middle string) somewhere in a melodic element that goes over the G chord!
Let me know if you have any success with Lydian chords, but you might also have a look at Gary Ewer’s other GREAT articles on Modal Chord Progressions, linked on his blog below the article.