OK, here goes:
1. Install iExplorer
if you don't already have it installed. Plug your iPad into your computer and open iExplorer. Navigate to the Apps -> ShutterSnitch -> Documents directory.
2. Select everything in there, except for the fileinfo.sqlite file. (Select the top file, hold down Shift, click the bottom file. Then let go of Shift and press Cmd (or Ctrl on a PC) and click the fileinfo.sqlite file).
3. Make a backup-folder on a drive on your computer that has enough space for all the files. Then drag the selected files from iExplorer to that folder.
4. Close iExplorer and go to the Home screen on your iPad and find ShutterSnitch. Press and hold the icon for a while until the icons start to wiggle. Tap the X on ShutterSnitch to delete it.
5. Press the Home button to stop wiggly-mode and go to the App Store. Find ShutterSnitch in the "Purchased" section and re-download it.
*** Important *** Do NOT open ShutterSnitch yet. Let it install, but don't touch it!
6. Open iExplorer and navigate to the Apps -> ShutterSnitch folder. You'll notice that the documents folder is empty. Select all the files from the backup directory on your computer and drag them back into the documents folder in iExplorer.
7. When the copying is done, you can open ShutterSnitch on your iPad. You'll get a couple of dialogs in your face. Don't touch the "Skip" button, but you can dispmiss the "Tip" dialog.
After a little while (or a long while, depending on the size of your collections), ShutterSnitch will start up and let you type in your "new" super user password - type in the original one you picked when you first installed SS. Go through the setup and you're done.
Note: doing this, has effectively wiped all your ShutterSnitch settings, so it would be wise to go through your normal use-cases to avoid surprises when it "really matters".