If you are not in the habit of doing commits in a particular way, and you don't mind doing a bit of scripting, this is what comes to mind -- I will probably do something like this myself, though I am using HG and not SVN...
Get the command line interface for Jira, rig it up so you can download 'my issues' into a list, parse the list with a script to create separate *.issue files that get dumped in a directory. Then as you work on issues, you move them from that directory, to a 'done' directory. When you are ready to commit, you run another script that creates a template for your commit message which includes all the done issues -- then you fill in the blanks for each issue.
You don't even need the CLI really, if all your *.issue files are associated with a script that will delete the file and add its ID to a commit template, then you can just create your own ID.issues files by hand. (empty files)
All that would be left is to script the commit.