On my large list of criteria for how you tell the difference between a musical and an opera: If the composer did his own orchestrations, it's very likely an opera.
DR Elmore, you say you can't buy the above, but I bet you do. In your post, you refute a lot of points I did not make. For instance, you ask if Babes In Toyland is an opera because Herbert did some of the orchestrations. Of course it isn't; I never said it would be.
I said I had a large list of criteria for what makes a thing an opera rather than a musical. One of the dozen is that it's exceedingly rare for a composer to do the orchestration of a musical, not so rare for an opera.
Let's put it this way: Think of 100 works in which the composer also orchestrated. Are most of these operas? Then, you agree with what I said: "Chances are, the composer-orchestrated work is an opera."
I don't recall all the other criteria, but I could look it up, if you'd like. Musicals, these days, play eight shows a week (Joy's plays twelve); operas, never that many. Now, you can run out and find some musical that plays less than 8 per week and say I said it was an opera. But, in fact, I said no such thing.