1) Right-click the project and goto Properties
2) Goto the "Flex Applications". There you will see all the files that are marked as Applications.
3) Select the new Applicaion file and click "Set as Default". When you click "Run" or "Debug" it will use this file to launch your project.
4) Click on the old Applicaion file and click "Remove". This won't delete the file.
Hope this makes transitioning to a new project easier.
Also remember to remove any styleName properties from your old Application tag.