I know nothing about this, but AFAIK with Google LDAP, a client certificate is mandatory, and FreePBX LDAP does not support client certificates.
The workaround as described in the document you linked is to use stunnel as a proxy, which should not be hard to set up. However, it appears that you have not yet done so.
This is supported by the library used and would probably be a good feature request. It would also be a simple community contribution as you essentially need to copy some files and change a few lines…