Build a websocket API through Amazon

We need to leverage Amazon API Gateway and Amazon Lambda to host a websocket bidirectional service that notifies our API's of received messages and that allow us to post messages to specific channels or groups. We want to use these cloud services to replace our hosted websocket connection. Messages In/Out are simple JSON structures (no binary data). The most important feature is that websocket maintains connection and properly routes messages to target group (users subscribed in that channel). Websocket should support authentication for client apps through APIs to our server. In order to connect the client needs a token and in order to connect to our API the request needs a header basic security validation. This should allow us to verify that the remote user is the genuine owner of the account/connection. Since websockets is new for us we need a savvy professional to guide us in the best practices of setting up our backend endpoints and API contracts for bidirectional communication This is a joint project. Also, it can be done through amazon or through google cloud, as long as it allows us to Post requests via Rest and to receive requests in the same way. The budget is aprox $200 usd and will be paid after complete functional validation (developer should deliver and help setup on our project cloud account but can host in his dev account before payment). The maximum time allowed is 15 days. The websocket needs to be fully functional by the first week of September. Full documentation is expected.