Go figure... ask a certain number of audiophiles a question and you'll get an equal number of answers.
Here's my take:
The dulcimer, like the piano, is a percussion instrument which has two basic tonal elements going on. You have the initial strike of the hammer and then the resonant response of the string/chamber/soundboard.
When afforded the luxury, I like to capture an instrument like this with multiple sets of mics and blend them to achieve the final sound.
If money is no object, a binaural setup is fantastic for capturing the perspective of the instrumentalist. I've had great success with the Neumann's KU-100 positioned just above the head of the musician, centered on the instrument.
In lieu of such a setup, I prefer to go with a matched pair of mics set up in an XY configuration. You might get some pleasant results with a pair of ribbon mics configured like this because of the bidirectional nature of the microphone pickup pattern. Royer's 122 is a personal favorite with Coles coming up close behind.
Then, depending on the quality of the environment, I'd set up a stereo pair of mics that, when blended with my 'close mics' will provide the desired depth of sound I'm looking for. With each of these setups, the distance from the source is going to affect the balance between the strike of the hammers and the resonance of the instrument. The further away, the less prominent the attack.
As with any setup using multiple pairs of mics, check the phase between the mics (left/right) and then between each pair. Adjust accordingly.
One other option that comes to mind is the Barkus/Berry 4000 Planar Wave piano pickup. I wouldn't use it as my sole source, but it does provide some different tones that can be very cool.
Oh, yeah. You can also get some fun results by setting the dulcimer on different types of surfaces. When the instrument couples with the surface, some interesting tones can be achieved. Of course, the inverse is also true.
Good Luck... Break a string!