Intonation Problems
Instruments- discuss specific features, luthiers, instrument problems & questions
At the risk on being a contrarian, I have had good success with keeping my dulcimer from going sharp as you go up the frets a different way that also helps with the bass buzzing problem. Rather than focusing on the saddle height, I find adjusting the nut or zero fret slightly higher allows me to keep a more consistent and lower action across the fret board. Yes, definitely, it sounds like your saddle is too high. When you get that resolved, and if you are in the mood for even more fine tuning, try raising your nut by maybe 10% and see if you can adjust your saddle down about the same percent. As with any adjustment, your mileage will vary.
Good luck and I think you are right in raising the nut.