To my knowledge, the original filenames are not present in the JSON data, however this is more an observation from watching what others have done, rather than extensive first hand investigation.
Several things come to my mind:
1: According to Photosynth's architect, the images are always sorted lexicographically:
2: I believe that Photosynth's log files contain the filename to image-number-within-the-synth correspondence. This will only help you for your own synths, as compared to the synths of others (since you have access to your own log files, but not others'). I assume you already know how to access your log files, but for others' benefit, open a 'Run' command in Windows (or a 'My Computer|Windows Explorer address bar) and type the following:
%temp%\photosynther to open Photosynth's working folder.