Hi Ian,
Apologies for the long delay in replying to your post. Hopefully you no longer get an 'Invalid request' error, but in case you do (or if anyone else reading this discussion has the same problem), we've found it to be caused by a temporary problem on the badgr.io site. When we tried again later, adding a badge from Moodle to backpack worked fine!
As you mention, you do need to check that the backpack settings are valid and that Badgr is correctly configured as the external backpack for the site, as otherwise this is another reason for getting an 'Invalid request' error (as mentioned in MDL-65545).
