Let me start of by saying I have not used JIRA before. I looked at their site and it looks like they only allow you to use Subversion to check code into your online repository. If that is the case then you are most likely stuck with Subversion if you stick with JIRA. In this case I would contact JIRA and see what they can do. After all, if you are using them now then you probably have a service contract with them.
Now if JIRA allows you to upload files to an FTP repository then why don't you just use Mercurial locally and then upload your code via ftp? Mercurial has a mode where all of the changes are put into a .hg folder within your solution. That means uploading and downloading everything shouldn't be to horrible.
Another option would be to leave JIRA. Have you checked out http://bitbucket.org/? It is Mercurial's hosted code option. It looks to be much cheaper than JIRA but also lack a few of the features. If they happen to be features you don't use then you might be able to make the switch easily.