I'm pretty sure the problem stems from poor air circulation and I am starting to be convinced it's caused by internal ice buildup although that's not totally certain.
Here is what I have accomplished so far.
I saw a photo of the defrost timer online and recognized a corner of it as something I'd seen and thus located it inside the refrigerator compartment behind the plastic cover at the top.
Using a small screwdriver I gently advanced it until the continuously running refrigerator shut off and went into the defrost mode. Measuring the input current at over 6A I determined the heater was working (actually I didn't have to measure as I could see a good spark when I pulled the cord).
I had planned to move it out of defrost mode 20 minutes or so later but by then it had moved off of its own accord and the machine was running again but performance was no better.
So the timer was working or at least it was now. Could have been stuck earlier I guess.
We also do not know if the heater stayed on or if it's intermittent.
This morning I put the timer into a defrost cycle again and I could hear sounds like bits of ice falling in the evap compartment. Again the timer moved on and the fridge restarted.
Afterwards if anything the air flow (as noted at the back of the freezer compartment) was worse. The melting ice must have dropped to a place where it's clogging air flow more than before. And if out of touch of the evaporator and defrost heater it's not going to melt and the defrost terminating thermostat will turn off the heat once there is no more ice on the evap itself.
So we have the following suspects:
Previously stuck defrost timer allowed this much ice to build up Intermittent defrost heater Defrost thermostat shutting off heat too soon
Unfortunately there's too much in the freezer right now to shut everything down and give it a thorough meltdown. Or even to access the evap compartment.