I migrated to Cloud Sites several years ago as it saved me a lot of money in monthly hosting fees for a dedicated server. Rackspace Cloud Sites is a PaaS offering from Rackspace that comes with the attendant limitations of PaaS - the main limitation being that you lack the features of having root access to a server and to be able to add any repos.
Anyway, I purchased Xenforo Enhanced Search before I realized there was an ElasticSearch dependency and there was no way to install on my Rackpace Cloud Sites account.
Fortunately, Rackspace offers ObjectRocket which offers ElasticSearch as a Service. It'll cost me $30/month but that's a reasonable cost for me for the capability. It also had the benefit of being another Rackspace service so it was on their ServiceNet and requires no internet traffic to get to my ElasticSearch node.
The problem I experienced, however, was that ObjectRocket required a username/password and the XenForo addon assumes that the ElasticSearch instance rquires no authentication.
This was solved by passing the username/password in the path itself. It looks like this: