Hello,
I agree that it is weird that whenever you look at the webcam it is spiking the CPU usage. However webcams are a separate function from Klipper entirely. When you preform a firmware restart, you will notice that the Klipper control panel is unusable, however, the webcam is still streaming. I mean this by saying it is most certainty Octoeverywhere sort of “distracting” Klipper, what makes Klipper fail. Not Octoeverywhere actually just causing the print to fail. It is more of a cause than a direct problem. I hope that’s a good example. 
This thread had a similar issue with Obico: MCU shutdown with BTT CB1 - #16 by Nem0815. There is also the board that you are using, a Pi Zero 2 W. It has about 20% less cpu’ness than the Raspberry Pi 3B. Meaning that it could hit 95 percent load when a 3B would only hit 75 or so under the same conditions.
You can also try to update the Crowsnest err. . . file? Anyway, it is described how to do it here: Upgrade from v3 to v4 - Crowsnest This may help as well.
I had a very similar issue where my print would randomly stop. And I always got the same “Timer Too Close” error. Usually a timer too close error means that something has gone wrong with the communication between the mainboard and the klipper host (Raspberry Pi or other). I would try to update the mcu fw as this is what solved it for me.
Hope This Helps,
Blake
Ps: I use Octoeverywhere with no issues whatsoever, so It must be able to be solved.