As Ian "ChaosX" Moris explained, implementing this clever trick took just an afternoon of planning and engineering to get working properly, something Sonic Team never did in the original release. After that, he spent a few days readjusting the smaller cutscenes and animations that had originally been created using the old mouth setup.
ChaosX is the creator of Sonic the Hedgehog: Project '06 (also known as Sonic P-06), an in-development remake of 2006's Sonic the Hedgehog that adds bug fixes, new features, and upgraded graphics. The project even has its own Wikipedia page, and you can watch the newest demo and access download links in the description: