What are the right settings to use S3 bucket (with non-Amazon URL)?

Did you read this yet? I struggled with setting up S3 and Cloudflare as well but eventually figured it out. You can still use Cloudflare for its security benefit, but I’m pretty sure you need a separate CDN service as well. Cloudflare isn’t like a normal CDN, it works differently. You should move to a cheaper S3 service, Amazon is expensive.