Most of those bands could be listed under the umbrella term of "fusion" or "world fusion", a blend of influences and traditions from multiple cultures. If there's rock, jazz, or electronic instruments involved, it's no longer (historically) traditional music. Anyway, this is a fairly circular argument, since all of those styles refer back to European folk music on some level - rather than being disjoint. And so-called traditional European folk music is not exempt from external influences - would you say the violin was invented in Norway?
Thus it doesn't bother me on principal, if folk fusion is reminiscent of jazz, but I will say that I've rarely heard this done well. Matt Howden's project, Sieben stands out in my mind, while most of the Nordic attempts seem to fail miserably.
I know what you mean by the word "neofolk," although in my collection I use the term far more loosely. It allows for easier organization, if I don't have 20000 separate genres
So in keeping with the topic of the original post, here are some diverse suggestions:
Blood Axis - incorporates many styles: classical, industrial, folk - Blót: Sacrifice in Sweden (1998)
Hagalaz' Runedance - sort of ambient folk music with pagan references - Frigga's Web (2002)
In Gowan Ring - psychedelic/progressive folk music, quite poetic - Hazel Steps Through a Weathered Home (2002)
Мельница/Melnitsa - Russian contemporary folk; alternately fun and melancholic - Перевал/Pereval (2005)
Sieben - electronic violin-driven music; intended for live improvised, one-man performance - Ogham Inside the Night (2005)
Sturmpercht - part music of the alpine region, part of their own creation; it's unique - Geister im Waldgebirg (2006)
Tenhi - Finnish progressive/folk rock; I only recommend Kauan (1999)
Vàli - instrumental acoustic music; drawing from traditional Nordic folk - Forlatt (2004)
Also I'd recommend the John Barleycorn Reborn compilation, for a collection of mostly underground folk artists, interpreting traditional British music in some surprising ways. The label seems to have shut down.