The biggest culprit to dulcimers going out of tune is the bridges shrinking and swelling with changes in the humidity of the environment. Wood shrinks or swells across the grain which in the case of the bridges is the height. Any change in the height of course changes the tension of the strings, and the dulcimer goes out of tune. This is the point behind lamination. Plywood is built up of layers of wood glued together with grain directions at 90 degrees to the layer above and below. This effectively stops wood movement, and the thinner the laminations, and the more plies, the better.
As an option, we make bridges with a core of birch plywood and solid walnut on the outside. You can see the ply core, but it isn't objectionable. The ply core limits the shrinkage or swelling of the bridge, and really helps with tuning stability. They aren't perfect because the dulcimer is still moving underneath them, but they really help. They don't affect the sound at all. I had a set on my dulcimer that I played every week all last year, and it stayed well in tune. Some weeks, it didn't need tuning at all.