Version v6.2.0 comes with a very handy feature allowing to clone multiple issues at once.
Jira Administrators have the ability to clone issues and move them to different project. Just select multiple issues and while cloning choose different project (since: v6.4.4 regular users are able to clone issues as well).
Select multiple scheduled issue, use "Clone Selected" button from bulk operations.
Add prefix to SI name
Create new description
Choose desired project
Use Clone button
If everything goes smooth you will see a confirmation message in top right corner:
If scheduled name is duplicated in given project, there will be an error message visible