Would building it yourself be an option?
I built this from a kit many years ago:
The hardest part was cutting out the sound holes and gluing up the body, which you wouldn't have to do on a solid body.
A solid body dulcimer would be a relatively easy build.
There are several humbuckers for mandolin that would be about the right size. But I wonder how effective those would be, because of the odd string spacing on a dulcimer. A small bar type pickup would probably be ideal.
Hmm...interesting idea. I wish I had my tools here