thanks for taking the vids, it does help describe what you are talking about.
The first thing that hit me was pure shock about the kind of snow you were stuck in. There is no way my truck would get stuck in that situation. That makes me blame the tires right off the bat. They look like a more highway oriented tire, and maybe thats the reason why the truck is doing so bad and also why electronics are kicking in too often/soon? Regardless, I tend to agree with you that in your situation, taking everything into account (tires, snow, terrain under snow), you were better off without ATRAC. I really do think better tires would make the system work more efficiently, and close that gap somewhat though.
Are you able to turn off ATRAC on your 4runner? I knew later ones had a "VSC off" switch, but didn't know defeating ATRAC was possible on any 4R...
Also in regards to the tire debate, I am a FIRM believer in snow tires. I was on the fence about buying a set for my truck, but decided on a "severe snow" rated all season (GY-W-SA). Not even close to the same performance in terms of traction, cornering, braking, etc. on the roads. However, I might agree that an aggressive AT tire is better in deep, untracked snow.