iCloud storing "lost" reminders?

I have a lot of troubles with the Reminders app, and have since the initial upgrade way back with iOS13. In general, my Mac Mini M1 2020 (running macOS Ventura 13.0.1) syncs flawlessly with iCloud. If I make changes in the app or in Safari (via Reminders in the browser iCloud interface), the changes update nearly instantaneously.

However, on my iPhone SE 2020 (running iOS 16.1.1), reminders do not sync either to or from iCloud. I've tried everything that the Apple Support page lists -- in fact, I've tried those steps 8 or 10 times over the last several years, over a series of different iPhones.

I've come to believe that something that I cannot see is wrong with my iCloud account, at least in terms of the Reminders server. (I use iCloud for pretty much everything else, and it syncs perfectly with all other apps: Photos, iCloud Drive, Notes, etc.)

Today, thanks to functionality with the new browser iCloud interface, I noticed this:

(Forgive me the blacked out portions -- they contain personal information.)

What I see there at the top of the Reminders list are two ancient reminders that are not in any Reminder list, which shouldn't be possible. Moreover, I cannot access them in any way. If I click on the Reminder widget in the browser, it brings me to the first Reminder list I have. They are not in this. When I search for them in the Mac app, they do not appear. The only reason I know they exist at all is because they continue to show up in this browser iCloud widget.

Does anyone have a clue of what might be going on here?

My iCloud Reminders issues have been going on so long that, at this point, I'd be willing to suffer a backend purge of my Reminders, if such a thing is possible. I feel like I need some sort of "full reset" of my Reminders information in iCloud, and I know of no way to accomplish this from the user end.

Thanks for any thoughts or help!