Did you also read the part on the first link that mentioned DNS?
Google education edition with 1.9.9
When using Google Education Edition with 1.99
The latest php mailer is paramont. If someschool.edu email at
google is not accepting mails from the moodle as valid mails you need to
create an SPF record at your host, allowing mail from the Central Mail
server, Google and the local server which satisified Google's validation
@ 14400 IN TXT "v=spf1 ip4:174.121.161.XXX
include:aspmx.googlemail.com mx:c1.hostname.com ~all"
This bit is server side more than moodle so if you are on managed
or shared hosting the server admin will have to do the record (try
submitting a request to have the record added with full details of how
and why to do so) then follow the previous the directions in this
While above is about a lower version of moodle and google edu, could have done the same for your now moodle host (which is different from Windows server I would assume) and it's something I mentioned before that yoiu might try. True, moodle server isn't a mail server but it does send mail if using forums etc.
And, there's the limitation ... does the site use the Front Page forum to which all users on the system are subscribed? I did see announcements on the site. How many users do you hae on the system?
As long as one stays at 1.9.19+, can live with the limitations, and doesn't migrate the server upwards to 2.x or 3.x you might be ok. Make note of it ... keep the note for when you do move higher.
'spirit of sharing', Ken