But still no WebSocket support?
If you want websockets you should be using EC2 https://aws.amazon.com/blogs/aws/new-aws-application-load-ba...
The EC2 ELB supports websockets and HTTP/2.
The point is that CloudFront can be used as the front end to your web site, with, depending on path, requests going to origins that are S3 buckets, ELB or EC2. Until recently, ELB didn't support websockets either. It does appears though that a new ELB was launched last month that does support it, so that allows for a solution.