The joys of legacy coding. The blockquote tags have been causing ugliness in RSS for a while, thanks to some coding in older parts of the site. An inability of the plugin that handles formatting to deal with paragraphs in blockquotes hasn’t helped.
Removed the blockquotes from older parts of the site and replaced them with their own div style instead. This allowed me the fix the weirdness that was happening in the blogs.
Blockquote tags need to be wrapped around each quoted paragraph. That way the RSS doesn’t have to deal with the extraneous br tags in its output, which looks much cleaner.