Snapshot Pro - Access Issues with S3 Bucket

I am running into S3 access issues similar to what John experienced in this support ticket:

https://premium.wpmudev.org/forums/topic/i-keep-getting-an-access-denied-message-when-connecting-to-amazon-s3

When I try to select the bucket after putting in my access ID/key, I receive this error --

Error: Could not list buckets :Access Denied

When I test the connection, I get this error --

Connecting to AWS
Using SSL: Yes
Setting Region: US West (Oregon) Region (s3-us-west-2.amazonaws.com)
Using Storage: Standard
Using ACL: private
Sending file to: Bucket: : Directory: Error: Send file failed :400 :

I have a bucket policy in place I believe is correct, because I'm using a similar backup plugin on another site and not having any issues.