Perhaps you might try running your own URL shortening/editing system (FOSS like ‘YoURLs’ perhaps: https://yourls.org/) and providing links on the LMS via that. Using the intermediate layer of Yourls, you can change the end point of the same link any time you need, or simply generate a new one.
Just an idea that might result in a faster turn-around than Zoom developing a whole new system/method.