This topic comes up every couple of months and always ends up as a stalemate. Some swear you can and some swear you can't.....and some just swear. And now we can't agree on what constitutes a fair and equitable test! Funny!
I've never weighed in on the subject but have some winter downtime somewhat random thoughts on it.
First off, I don't have a good ear for this type of thing and can't tell the difference between a teardrop and an hourglass.
But of course there are people who can.
A couple of extreme examples who come to mind are Antonio Stradivarius, in the 1700's, and Lloyd Loar, in the 1920's. They built violins and mandolins, respectively, and refined the shape and sound of their instruments and no one has been able to better their designs. I think they'd have the god given ability to detect acoustical differences in the shape of dulcimers.
But I don't believe you have to be a world renowned acoustician to tell the difference. Mark Gilston, John Keane and Ken Bloom are three who I think can. And there are others. I'd put a little bit of money on Dwain Wilder and Richard Latker.
Can a dulcimer builder adjust an hourglass shape to have some of the acoustical properties of a teardrop? Sure. And vice versa.
I remember when I got my first dulcimer after playing guitar for a few years and I thought "how can that thing work"? It has a big fingerboard running over the top of the soundboard. What a poor way of transmitting sound. But we all know it works. But we don't know how it works yet.
Someone will come along one of these days and figure it out, and hopefully will have the personality and communication skills to let us in on it.