I found a work-around to this problem, albeit a really bad work-around.
I got into File > Preferences > Fonts, and then unchecked EVERYTHING except for one working font (such as Verdana and it's variants).
Now Scribus does not keep switching to a strange font from the top of the list, because the top of the list (and the only thing on the list) is Verdana. Then when I export to a PDF, there is only one font to embed, Verdana, and it works without issue.
Still ... I would love to know the source of this issue. I don't believe I had these problems with the 1.3.x branch?
Thanks,
-Steve Ballantyne