Relationship Among String Height, Intonation and "Zing"

In noter/drone playing, I'm curious about the effect of string height or action. I've heard here and other places that generally higher action works better for noter playing. I think I've witnessed the reason, but I'm not sure. Several months ago I had the opportunity to play what I thought would be a great, modern, diatonic(!) dulcimer...perfect for a good all-round noter/drone dulcimer. Unfortunately, it has so much "zing" when moving from fret to fret that it was really not pleasant. I know we all love a little characteristic zing in our noter playing, but this was crazy. As I recall, the action was fairly low on it, and I'm wondering if that's not the problem. Does the lower action tend to cause the strings to interact (actually buzz) on the next higher fret more than we want as we move between frets with the noter? The dulcimer was probably great for chord melody....no buzzes at all when played that way.

So let's assume that we raise the bridge on the above instrument. What does that do to intonation? Now we have to stretch the string a little more to fret it, so I assume it will go sharp. If this is correct, is it likely a problem mostly on higher notes near the bridge where we have to push down harder than for the lower notes?

I think I have reasonable technique with the noter; not leaning on it between notes, etc. I don't notice this problem at all with several other dulcimers here played in that style.