Ok, I have a little more light.
I understand now why there is a difference between copy/pasting and drag and dropping from Word to the WP editor. WP intentionally intercepts the c/p process to scrub the tons of garbage markup that MS insists on inflicting on the world, but d&d does an end-run around that utility.
I also found that it apparently is imported snippets that are messing up para spacing. This time, while in the WP editor I brought in Bible verses from Logos rather than blueletterbible, but as soon as I did the next linefeeds lacked the spacing the previous ones had. Because the drop-down para style box in the WP editor is pretty lame regarding changing existing text, the solution was to switch to html view and clean up the code there. Once I did that, successive new paras had the correct spacing again.
At that point I transferred over to Word and completed the piece. I then c/p'd over to the editor, and everything transferred beautifully. I think the key is to work very cleanly regarding linefeeds when changing para styles in Word.
The c/p operation maintains font markup such as bold or italic, but nukes styles, so that all styles come over as Paragraph (when in Word, I'm composing in .doc format, not html). So I have to go through and apply such styles as Blockquote manually. But that's not too bad a task.
Bottom line: I need to keep style transitions from snippets clean, and there shouldn't be much of a problem.