Just because something CAN be done, does that mean it SHOULD be done? Sometimes.
I've been thinking about this idea for some time now, and I finally got around to trying it out. I've had this homely, misshapen teardrop dulcimer hanging on the wall for years now, and now it has become a homely, misshapen teardrop dulcimer that folds in half for storage or shipping! I'm happy to report that it was not one of MY handmade dulcimers that underwent this surgery, but rather an ultra-cheap one I bought on eBay. So it's now a proof-of-concept instrument, and it actually works! It sounds just as good as it ever did, to my surprise, yet when the 3 strings are slackened and unhitched from the tailpins, it's a simple matter to then release the side-mounted draw catches, and fold it in two. Now it can fit in a container (such as a small toolbox) of 6" x 7' x 18" interior size.
To return the dulcimer to playing configuration, I unfold the body, ensure that the tongue of the fretboard joint is in place, clip the draw catches, and rehook the loop ends of the 3 strings to their tailpins. Now I just tune up and go!
I'll take some pix of it soon, but... IT AIN'T PRETTY.