In case it helps anyone who stumbles across this problem.
The solution is setting the BO rule properties so it doesn't run on the server and 'No' form initialisaton.
Then you don't get the warning message in the configurator when you're saving. And it doesn't cause a problem when it runs.
Your 'Warning Message' will display when the user enters stuff that requires a Warning, but still allows them to continue and saves the record when they press Save.
I don't know about Display Message from a process though, as I'm only doing directly in the BO Rule.

It would be cool, however, if the Display Message function had a few aliases, like Display Warning, for eg. Then the Title of the message box would be, for eg, 'Warning' instead of 'Information'