Grant Relay Account SendAs on behalf of ALL users

I've set up an IIS SMTP relay in order to forward mail from legacy devices / services to Office 365 using a dedicated account we'll call relayaccount

I've noticed that for the relay to work properly for any user, I have to do:

Add-RecipientPermission %useralias% -AccessRights SendAs -Trustee relayaccount

This is all well and good, but what I'd REALLY like to do is set this up so that the relay has permission to send on behalf of all Domain Users (or another security group containing Domain Users).

I've created a mail enabled universal security group we'll call rgmailrelay and given it an email address of the same in the AD attribute editor.  I then ran the Add-RecipientPermission commandlet above to grant relayaccount SendAs permission for that Security Group and added Domain Users to the group in AD.  This is not working though, and I'm not sure why.

What am I doing wrong here?  Is there a way to accomplish what I'm after?

Thanks!