Most McSpadden dulcimers have what's called a compensated bridge (this is the white plastic piece furthest from the tuning pegs). They set them up specifically for DAA or DAD tuning. Try retuning to DAD and see if that helps the intonation issues on the melody string(s). If you find that the intonation up the neck is better in DAD than in DAA tuning, then that's likely the issue.
My resolution to this, because I retune frequently between DAD, DAA, DGD, EAE, etc. is to have had a non-compensated bridge installed on my McSpadden.
If that's not the issue, then it could be that the bridge and/or nut (the nut is the white plastic piece nearest the tuners) may be too high. A good luthier/ stringed instrument repair person can take care of that for you.
I suppose it could also be that the frets are placed incorrectly. That happens if the instrument was built from a kit rather than manufactured by McSpadden. I've never seen it on a factory installed job, though.
Hope this all helps.
- Sean R-B