I recently purchased a teardrop Fred Martin dulcimer on eBay (unsuccessful in finding an Edsel Martin). It has an inordinately long body and scale length (longer than even my baritones and bass dulcimer). No case or bag I own will fit it: I tried using an old guitar gig bag and the body area is too short and neck area too slim. The person who used to make custom cases to fit the Edsels has retired (or passed on, as have Fred and Edsel). I have a large and heavy Blue Lion oblong hardshell case, but it's fitted inside for a heart-shaped standard-scale Blue Lion; moreover, the Martin Bros.' pegheads tend to rise taller than most scrolls, so I doubt that the lid would even close.
If you make custom gig-bags or cases for dulcimers (or have a pattern I could use to "recycle" an old cheap quilt), give me a shout. (I saw a used Mark Leaf guitar case on Elderly's site but it was still twice what I paid for the dulcimer and fitted inside for a dreadnought guitar.