This is mostly just a bug report since I've solved the issue for myself - I just picked up a Synology DS115J and updated it to DSM 6.0-7321 Update 6. I proceeded to install Sync 2.3.7 for the ARMADA 370, but the package would not start.
Running the package manually (sudo /var/packages/bittorrentsync/scripts/start-stop-status start) failed with the following errors:
su: Permission denied
Your account has expired; please contact your system administrator
The script is attempting to "su - admin", but looks like it is expired and/or does not have access to perform this operation. I'm assuming this was intentional; I tried resetting the expiry with the synouser command, but was unsuccessful.
My solution was to just just start it as root:
#su - admin -c "umask 000; PATH=${PATH} ${BTSYNC} --config ${CFG_FILE}"
umask 000
${BTSYNC} --config ${CFG_FILE}
The package started perfectly from the DSM web interface:
Enjoy,
-Lulzon