I would encourage anyone with the 42RLE to go out and perform their own test by accelerating from a stop with O/D OFF and with O/D ON. You'll find that with O/D OFF, the TCC will lock up immediately after the 2-3 shift occurs. With O/D ON, the TCC will remain unlocked in 3rd gear and lock immediately after the 3-4 shift occurs. I'm not saying that we should leave O/D ON or OFF, rather that we need to know when to leave it ON and when to turn it OFF.
In the first video above, if the drop of RPMs down below 2,000 is happening after the 1-2 shift, I would still say that the PCM has placed the transmission in extreme overheat mode. On the other hand, if this drop in RPMs is happening after the 2-3 shift then it's because O/D had been turned OFF before the transmission shifted into 3rd and this drop is due to the TCC locking up in 3rd gear.
I've had my LJ since 2012. Since purchase, it's been driven just about every day, over 170,000 miles. For the first 6 months I followed the advice to turn O/D OFF unless I were on the freeway. Without considering the shift behaviors at the time I noticed 2 quirks: The first was that there was a sudden dropped in power after the transmission shifted from 2nd to 3rd, like a dead spot. The 2nd was that the transmission would lug at 30 MPH, even violently if going up hill.
If you start out with O/D OFF, the TCC will immediately lock up after the 2-3 occurs. If you've reached your target speed, fine, you'll only end up lugging the engine. If you to continue accelerating however, the TCC is going to unlock. Now instead of the transmission only performing a single action, it's performed 3: 2-3 shift, TCC lock, TCC unlock, and it will do this every time it shift from 2nd to 3rd gear. If there were a predetermined number of times the TCC could lock and unlock, you'd be cutting the service life in half if always starting out with O/D OFF.
If you start out with O/D ON, the TCC will not lock up in 3rd gear (at least not immediately), keeping the direct drive, 1:1 ratio. Not only is the 2-3 shift now resulting in only a single action, your RPMs will also continue to climb while accelerating instead of dropping as the TCC locks up.
Rather that starting with O/D OFF, learn when to turn it OFF and when to turn it ON. In my experience, it's best to start with O/D ON, then turn it OFF after the 2-3 shift occurs, while still accellerating. Then, before the 3-4 shift occurs, turn O/D OFF so that the TCC locks up in 3rd with the RPMs high enough that they won't drop down below 2,000. If you're at your target speed, that's it. If you still need to accelerate you can do so with the TCC lock up in 3rd and then turn O/D back ON when you're at a speed high enough that the TCC will lock up and remain locked.
O/D OFF = TCC lock up in 3rd
O/D ON = TCC lock up in 4th