Hi Andrew Mundt
I'm glad that you were able to resolve your issue and thank you for posting your solution so that others experiencing the same thing can easily reference this!
Since the Microsoft Q&A community has a policy that "The question author cannot accept their own answer. They can only accept answers by others", I'll repost your solution.
Please click "Accept" the answer as original posters help the community find answers faster by identifying the correct answer.
Issue: How to fix "Can't manage CORS on this resource. Please select another storage resource." error.
Resolution: It appears that the CORS rules take some time (more than minutes) to take effect. I suggest that there be a notification about this.
Please don’t forget to close the thread by clicking "Accept the answer" wherever the information provided helps you, as this can be beneficial to other community members.