OK, turns out there is a "secret sauce" in the recipe I was unaware of at the time. Before doing the View Page Info steps I described, you have to play the station momentarily first with the Play button--THAT apparently is what populates the Audio info, as shown below. I assume that will also make it show up in the other method.
Okay sveakul, you have redeemed yourself. :-)
I tested with your Yellowstone link and it was successful. Then tried two others, again resulting in success.
Then I tried a tough one - CBC Radio One. Years ago they had published their live stream URLs on their website. Then they moved to TuneIn. Since I use a Squeezebox, I had to plead with them repeatedly via email to give me the URLs. At first they wouldn't. Then I got one. I asked for three more and eventually got them. But now, with this method, I can extract them from TuneIn.
Great big thanks!