Bingo. I still love ALL the individual service techs, they've all been awesome, and I have to emphasize that. Even the call center people are good now... when I reach them.
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So, I have VERY good news. Thanks to those who gave me a contact point. I have gotten a response from management which thanked me for my "tactful" letter, and I have a way to follow up.
I think in this case management awareness is probably 100% of the problem. Though the proof of the pudding is in the eating; we'll see whether the phone tree gets fixed promptly. (And whether chat reappears, and whether the list of service centers acquires email addresses, and whether voicemailboxes stop being always-full, and so on.)
I think people talking about the current "model" are missing the point. The real disaster was the catch-22. It's great to get as much as possible automated, but not everything can be. When the online or app options don't work (my preferred service center could only be scheduled by phone, and I couldn't find the email address listed), the remaining customers go to the phone. When the phone tree makes it impossible to directly reach the call center, which still exists, something has gone terribly wrong. I hope my letter gets the phone tree fixed.