It's been six months since I posted this thread. The SlingPlayer for Android's ability to cast to Google Chromecast had worked great until months before that, when a particular software update had broken it. Another user had identified an obscure workaround; I found that and reposted it.
Another six months have now passed and, unless I'm missing it as I search this forum, Sling Media has continued to say LITERALLY NOTHING about this. NOTHING. SILENCE. User after user posts questions and complaints about this same issue, and the company responds with NO RESPONSE WHATSOEVER. Utterly pitiful. (Fortunately, the workaround still works.)
I don't care much for a company that shows this level of contempt for its paying customers. Somebody out there, please buy this company and instill the concept of customer service.
Sling Media, if you have made any statement contrary to what I've written here, point me to it and I will be happy to delete this post.