For some reason, [Jira]'s [formatting] is not Markdown. Since you write everything in Markdown, you might be looking for a converter. If you furthermore hate node.js as much as yours truly, the search can easily claim your soul. Rest assured - I think [mistletoe] is the answer we are seeking. It is a pure Python Markdown parser which can render the parsed Markdown in any format, and one of them is Jira. It even comes with a [script] for this exact purpose.
[Jira]: https://jira.atlassian.com/
[formatting]: https://jira.atlassian.com/secure/WikiRendererHelpAction.jspa?section=all
[mistletoe]: https://github.com/miyuchina/mistletoe
[script]: https://github.com/miyuchina/mistletoe/blob/dev/contrib/md2jira.py