Is there any way to convert markdown to asciidoc (or be able to produce the same HTML output)?

To echo @akosma comment, pandoc does indeed have AsciiDoc support:

# Convert to AsciiDoc from Markdown:
$ pandoc -t asciidoc -f markdown file1.md > file1.txt

You can also go directly from Markdown to HTML:

$ pandoc -S -t html -f markdown file1.md > file1.html

(The -S just to produce nice curly quotes and other Smart typographical changes)

Try to use Pandoc to convert the markdown source to docbook xml.

From there, it should be possible to convert the docbook xml to html with the same technique as you used before for the asciidoc input, e.g. use the same xslt-translations for docbook->html.

In my experience, Pandoc doesn't convert a lot of documents correctly, so I've created my own converter, which can be found here.

It's a simple tool written in Java which has been successfully used to convert a lot of documents, including the manual from Geb.