You can change the document size! There is no need to create a new Illustrator file - this is false.
All you have to do is go to your tools > double click on the artboard icon > enter in the new size you want. You can also manually change the size by clicking on the "anchors".
By the way the artboard icon is just above the slice tool on the tool bar.
What about scripting a copy from the existing file and paste into a new document (created from a .ait of the correct size)? If your files are single layers, it shouldn't be too unmanageable to script.