Thanks duck and wolf. I did pretty much what you guys suggested, but I used a little utility called Balthisar Tidy to clean up the html, then I used TextWrangler to find & replace patterns that included the <br>s -- one pattern with <p>, another pattern with </p>. Balthisar Tidy was helpful in creating distinct patterns for one and the other.
FWIW, this is where I found Balthisar Tidy (free):
http://www.balthisar.com/products/tidy
I'm on a Mac. Better tools may exist for Windows.
... now if only I can remember what I did the next time I need to do it. (Set break-before-br to Yes, then replace a pattern including stuff BEFORE <br> with <p> and a pattern including stuff AFTER <br> with </p>. Replace "<br> blankline <p>" with "</p> blankline <p>" or something like that.)