Yes, try replacing the strings.

I have had more than one dulcimer, and I've played other people's as well. I think it's common for them to get whiny as you move up the fretboard. I like my dulcie warm and beautiful, so I don't tune it DAD. Me for DAA!

Don't use the high D to tune it, use some lower note. I haven't played for long time (hand problems), so I've forgotten which note I use, but I remember it wasn't a high note.

The beauty of the fretted dulcimer is how easy it is to play harmony on it. Hit lots of strings when you play and let it do its thing.