Saving data in Code Composer
In CCS 5 (and probably in v4 too) you have a "Memory Browser" option under "View" menu. From that view you can save/load memory from your target, setting the start address, data-type and length of your data.
The output will be a binary file, but you can easily make a script to convert it to text (if needed)

This way you'll still need to pause the target. But you'll not need to scrool through the whole buffer.