Good suggestions but I have found a simple solution for my needs.
To recap - I need to be able to have root-activated emails go out from a server w/o a real domain.
The solution for me was to modify some setting in
/etc/postfix/main.cf
In that file there are three settings of interest to this issue, myhostname, mydomain, and myorigin. Assume that the local host with no qualified domain is named LocalH and the external domain that is in existence is called ExternH, then the settings I ended up with look like:
myhostname = LocalH.com
mydomain = LocalH.com
myorigin = ExternH.com
where you would insert .com or .org or whatever is proper for your external FQD. With these settings any outgoing mail takes the myorigin data as both the ReplyTo address and the From address for message and it also pre-pends the current user so the actual From/ReplyTo looks like
External MX’s seem to like this and see it as a real domain and pass the message.
The only catch is that if you have a server with multiple users, which I do not, is that everyone is getting that From/ReplyTo address.