I had certainly never heard of this font before. I downloaded it and installed it, and it definitely has more characters I need than most fonts; so far, it has had every character I have needed. Since the only other font I've found that has them all is Geneva, it is a nice find.I am not an expert, but I wonder if the font set issue can make a bigger difference. I use Libertine http://libertine-fonts.org, and it does have some characters specifically for medieval fonts (Latin and Greek, and more scripts/fonts).
However, NisusWriter still shifts the baseline when using combining diacritical marks in this font. This would seem to demonstrate that the problem lies in the way NisusWriter does baselines. Since using Geneva or Libertine at least gives a uniform baseline shift, it's easier to compensate for it, at least.
Thank you for the suggestion.