First, let me say that your comments led me to a solution to this issue and for that I thank you. I spent the day listening to music instead of troubleshooting, and Roon’s discovery engine made that quite enjoyable.
The solution was disabling the DNS reflector I had enabled on my main server a couple years ago (and which I had also completely forgotten about until today). Sometimes I get a bit too big for my britches installing stuff.
However, a counterpoint: no other software I tested over the past six days had any problem whatsoever with my network configuration, including the DNS reflector. This is literally the first time I have ever even noticed it was there.
Roon is outstanding software, but all software has bugs. Frequently, those bugs only manifest themselves in unusual edge cases. I freely acknowledge that my use of a DNS reflector represents such an edge case, but the fact that no other software I tested in the past six days (and in fact over the past few years) so much as sneezed at this indicates that Roon is handling Chromecast discovery in a suboptimal way.
Your thoughts is this thread ultimately led me to a solution, and I am very thankful and pleased with the result. Thank you so much for sharing your expertise.
However, your comments regarding the issue at times bordered on apologism. Yes, I had an unusual situation that ultimately caused this problem for me. The fact that Roon is literally the only software that misbehaved in this environment does, to me, indicate some deficiency specific to Chromecast discovery in Roon.
Reporting faults, even in software we love… no, PARTICULARLY in software we love, is how that software gets even better.
Thanks again for your help. I’m truly grateful. I look forward to enjoying Roon for many years, and I hope you do as well.