I would avoid the display Import/Export as that actually converts a display to XML during the export so you can do editing before importing. Handy if you want to use an XML editor to do a search and replace. But, not necessary just to copy the display.
Use the Application Manager to backup/copy/delete the entire project. when you are done, your displays would be copied to another project, leaving you with the same scenario, how do I get them into my current app. Way overkill for what you need.
How about a composite of post #3 and #4, both of which will work.
Right-click on Displays and select Add Component. Then browse to the folder where your display is currently located. Select one or multiple displays and it will copy your displays from the source to the proper folder in your application. If you need to replace tag names, use the Tag Substitution option.
Opening two copies of Studio does work as agrosse mentions, but unless you need to preview the displays, is unnecessary.
OG