Why is Distiller butchering this rasterization?

I have a 300dpi PNG in a Word 2003 Doc.  I print to Adobe PDF using Press Quality -- 2400dpi, "Convert smooth lines to curves", and no image compression.  I've zoomed in on part of the image as rendered in Word, and the same part as rendered in Acrobat after printing, at which point it looks awful.  What can I do to preserve the image quality?

In Word:

And in Acrobat:

Don't know if it's relevant, but image source is a PNG from AI with transparent background and gradient set in Word.