Thanks @Thomas Wolf - Those are great things to try when having prompting issues. I've tried them without success in this situation.
Thanks @César CARDORELLE - That was my first try, but no success.
Ultimately, I would like the finalized report to show the customized prompt page when launched from the Cognos portal (without saved prompt values), but SUPPRESS the customized prompt page when invoked from a custom URL that supplies valid parameter values for all prompts. I believe that is the behavior that was intended to be enabled by the run.prompt parameter, but it appears to be defective.