I was able to restore my previously open files by opening Text Wrangler on the new computer, then quitting.
There was a file with a time stamp from before the migration (but now on the new computer) called: Sleep State-B19E6018-850B-520D-9E0A-602846B3758D.appstate
Text Wrangler generated a new sleep state file, which I dragged to the desktop.
I renamed the pre-migration sleep state file to the same name as the new sleep state file that was generated after closing Text Wrangler.
Then, I reopened Text Wrangler, and all of the files from the old computer opened.