I fixed the problem! My issue was as follows:
I created the bucket in the plugin using some capital letters. E.G. Example-Bucket
When the plugin created the bucket it went to all lowercase. E.G. example-bucket
Then (after a ton of debugging / tcpdump) I uncovered that the server/plugin was getting a 404 bucket not found error and failing silently. The plugin was using the bucket name with the capitalization, and there was no easy for me to fix that. In the end the fix was to delete the bucket and rename it making sure to use all lowercase letters.
It appears that this behavior may be a bug due to the unintentional outcomes of the issue.
It would also be appreciated if we could get some type of error message when the plugin fails to connect to S3.