Update on my situation...
I previously sent off bug reports and a message to Matt Mullenweg, neither of which produced a response.
However, I was just able to successfully commit my first changes to my plugin's repository. I received an email a couple of hours ago telling me that my repository would be ready in about an hour. I waited longer than an hour to be sure, and my commit took.
From what I can tell, these 403 error problems come from the fact that the accounts haven't fully been set up. They appear to be set up, but they are not. So, the documentation about the process and the process itself definitely needs to be improved. The documentation about submitting a plugin should indicate that you have to wait until you receive the email message and follow its instructions before being able to commit changes to the repository.
Anyways, I hope that every else experienced the same and that this process can be enhanced to prevent these headaches in the future.