I can't get your video to play, but these were the same symptoms my '01 was exhibiting. I had Toyota drop the pan and replace the fluid (not a flush). No luck. New (reman) transmission from Toyota at 245K miles.
I'm hoping this is not your issue, but thought I'd throw my 2 cents in.
What was your solution here? I've run into the exact same issue with the back bolt on the lower control arm. My wrench only goes to 150 ft lbs, think 166-170 is called for? I got lucky with the nuts not spinning, but was not able to achieve even 150# on the PS due to clearance issues with the...
Bobby Moran @ The Cruiser Co. In LR has a very clean '85 that might still be for sale. Has mild lift, 4cyl, 5 spd, etc. He's offered it to me several times in the last few years. Ask was very reasonable.
Odd that Toyota factory reman isn't available now. Steve Landers here in Little Rock installed one for me in Feb of this year. 2001 MY. Trans started slipping in first. 238K at the time.