I’ve been able to do some more testing while I work through my mechanical chime issue with Wyze, and the testing also involves the “Cameras as Chime” feature. Spoiler: The problems I reported in my initial post continue to be issues. 
I finally updated my Video Doorbell v2 firmware to 4.51.2.0578 a few days ago (I was able to do a direct update from 4.51.1.8444 to 4.51.2.0379 first; it skipped two updates but required me to get to 4.51.2.0379 before the app offered me 4.51.2.0578), since I’m throwing everything else I can think of at this thing in order to try to get it working normally again. This was after trying other solutions with limited success (and eventual failure) and finally resorting to the alternate wiring method. I figured finally getting the firmware “current” shouldn’t hurt anything and might be only temporary anyway.
Incidentally, the mechanical chime sometimes makes new noises with a doorbell button press, often a “ding-dong” accompanied by a rattle/hum sound from the chime box. Wyze Support said this about it in my ticket:
Please know that the buzzing/clicking sound on the chime is normal when an alternative wiring method is used.
That doesn’t seem “normal” to me, but then I don’t understand why this thing would work with the “normal” wiring for months and then fail, and then changing the wiring to the “alternate” scheme makes it work again (but not in a consistently “normal” way). 
Anyway, I also updated my problematic (the one I described in my initial post that still chimes twice even though I’ve deselected that camera as an accessory chime) Cam Pan v3’s firmware from 4.50.4.9222 to 4.50.5.0587. I rebooted the camera (even after the automatic restart) and then did some testing:
- Confirmed in the Video Doorbell v2’s settings that no cameras were selected for Cameras as Chime.
- Selected the problem child Cam Pan v3 as a chime.
- Cameras as Chime showed “1 camera” selected.
- Backed out to main Settings screen to Restart Video Doorbell v2.
- Also did Restart of Cam Pan v3 from its Settings.
- Confirmed after restarts that Cameras as Chime still showed “1 camera” selected.
- Went to Customize Cam Pan v3’s Cameras as Chime settings and selected Remove as Chime.
- Resulting Cameras as Chime screen showed “No cameras added.” message.
- Backing out to main Chime settings screen, Cameras as Chime still showed “1 camera” selected.
- Confirmed that it’s still necessary to back out one more screen to the main Settings and then tap back into Chime in order to see Cameras as Chime with a “Not setup” message.
- Performed Restart on Video Doorbell v2 and Cam Pan v3 and again confirmed that Cameras as Chime is “Not setup”.
- Once I saw that Cameras as Chime was correctly (?) displaying the “Not setup” message, I pressed the doorbell button. After a delay, the Cam Pan v3 made the chime sound. Twice.
It’s not the end of the world, but this thing—this feature—still isn’t working consistently in the way that I expect as a user: I should be able to reliably turn it off if I can turn it on.