The red button on the upper thermostat did not pop this morning, and
that may have been because I re-adjusted the 2 brand new thermostats to
their factory presets. Both thermostats are so-called "Apcom Style"
thermostats made as OEM by Camco. They are currently on sale at all
Home Depot stores for 3 bucks apiece, which makes me wonder if they are
crappy because they are so cheap, or they are so cheap because they are
so crappy. They are the exact same replacement models that came with my
Bradford White water heater, so I'm pretty sure my wiring is the same,
except I had a little problem tightening the screw on the black wire of
the lower stat because the screw offered some resistance so I forced it
and may have stripped it a little bit, but there is still some
electrical contact, I think.

Each thermostat has 4 settings - "Hot", "A" "B" and "C". "Hot" is the
factory preset at 120 degrees F. I turned the white knobs to "A" before
I installed them because I was guessing "A" might be at least 135
degrees F, which is supposedly the minimum temperature needed for the
clothes washer. Then I installed them. Shortly thereafter, the hot
water temp zoomed up to higher than normal and the red button tripped.
I reset the red button. Then I turned the white knobs back to "Hot" and
I heard a distinct click on the upper thermostat, as if it was closing
(or opening?) as I was turning the white knob back to "Hot" from A"".

It seems to that my act of changing the factory presets from "Hot" to
"A" prior to installation may have confused the thermostats. Perhaps I
should have installed them with the factory presets at 120 degrees F
before I decided to change anything. Just as a car needs a break-in
period, perhaps the thermostats need to be installed first before they
should be adjusted temperature-wise. Does this make sense?

Sorry for the long-winded explanation. I'm pretty happy now at the 120
degrees F factory settings, as long as they don't trip again. So I'll
suspend the element replacement project for another day. Thanks all for
your support!