Is there a way to add a service reference to these Web API endpoints and have the tooling create the proxy client and CLR types as it would do with a typical WCF service? I know there is no SOAP involved here but I did read that it is possible, just not how.
No it is REST service. REST service doesn't expose metadata for creating proxy by service reference (except WCF Data Services which have some special form of metadata). Use Web-API's
HttpClient class to call the service.