OTOH, given the massive publicity of the project, it would be difficult to keep it from getting reanimated at some point...
I don't see that there was massive publicity at all. Even viewing the Genesis video presentation required top-level clearance that apparently only Starfleet flag officers had. After the incident with Khan, the Enterprise
crew was ordered not to discuss Genesis with anyone. McCoy was arrested because he used the word in public (before assaulting another Starfleet officer). Kirk's after-action report was viewed in a closed session of the Federation Council presided over by Hiram Roth.
There was no mention of any involvement of the Federation News Service, nor was the incident mentioned again after TVH. Janeway references Marcus' involvement in the project when making a log entry about the Omega Directive, but she was a command-level officer with close ties to the admiralty and could have learned of the project through any number of means. There's nothing to suggest that what she knew was common knowledge.