Hi,
Here is a summary of information that we gathered from the web and from our Exchange administrator, who migrated our accounts few weeks ago. What you need to do is to allow impersonation of your service account as a malbox user. That is what you have already done following the instructions at http://cloudfinder.com/user-impersonation-settings-office-365/. In addition to this, you need to set permissions to make it possible to perform specific operations. By default, an account that has impersonation access is granted the "Send as" permission only. Additional permissions are "Send on Behalf" and "Full Access". So it seems that you indeed need to grant "Full Access" permission to your impersonating account, which is what you already mentioned. Here are some links to MSDN pages that lead us to these conclusions:
Permission list
https://technet.microsoft.com/en-us/library/jj919240(v=exchg.160).aspx
Impersonation
https://msdn.microsoft.com/en-us/library/office/dn722377(v=exchg.150).aspx
If you discover any additional information we are not yet aware of, please let us know.