Starting issue?

No don't just change parts, if your friend has a scan tool, have him monitor the speed sensors while driving to see if they are outputting the correct data. Do a full system scan, every module for codes.

I can see the Check engine light is on, what codes are stored in the ECM? I can't hear anything in the video, I would need to be in the car to hear it, but the ECM is setting a code, I'm sure that will give you direction, write down the code number, and I'll look up the criteria for you.
Just stop by AutoZone or another parts store and they will scan the car for free, just get the code number, don't let them sell you any parts yet.

Conductor plate? Thats a new one. What codes are set in the PCM? Are you getting an "Output Shaft Speed sensor", Input shaft speed sensor, wheel speed sensor, vehicle speed sensor, code? I don't see how a transmission guy can tell you what's wrong without even scanning or looking at the vehicle. There is more than one speed sensor in the vehicle, service info states your vehicle gets its vehicle speed reading through the BCM on the CANbus network from either the PCM, ABS/ESP module. So, it depends on what actual code is being set to diagnose the system. Limp mode is a safety mode.

Is it the 8HP45, 845RE or the NAG1? The first two Automatic Transmissions have 8 gears plus Reverse, the NAG1 has 5 plus Reverse. There are quite a few different setups with each transmission as well. There's a lot of information here, do you know if it's the 5 gear or 8?
Is there one bulk connector on the transmission? Maybe we can check the harness for any issues, On the 8-speed transmission the Output shaft speed sensor looks to be bolted into the valve body, all information transmitted to the transmission and back to the TCM is done mostly by a CANbus network. We can verify the Transmission Relay and fuse that power up the TCM, but this still depends on which transmission we're dealing with. The 5 speed has a smaller connector
With the NAG1 Tranny it states that there is no speed sensor internal to the transmission that directly measures output shaft speed, the ABS wheel sensors provide the output shaft speed.
So, did that code come from the ABS/EBCM module or was it from the TCM?
Is it possible we're dealing with a bad wheel speed sensor?

This is the OSS for the 8 speed transmission, it appears to be under the valve body, but its not clear if the sensor can be replaced without removing the valve body.

Okay, this is a really complex transmission. If there is a speed sensor fault, the code should also be stored in the ABS module, if it is, that at least will give us some direction here. For a 2wd, there are wheel speed sensors for each tire, one in each hub, sometimes the trigger wheel for the sensor is built into the wheel bearing. You can start by checking that the wiring to each sensor is not damaged. Service info doesn't say what type of sensors these are, there are some different codes for them though, and a flow chart for testing, but it would help if there was a code for a specific wheel. There is most likely some reference current or voltage monitored for it to be able to set these different circuit faults.
Is the ABS light on? Because it looks like the only other output shaft speed sensor is for the other transmission type. We really need more information on the code that was set. Without it, it's just assuming. If you can get the code number from your friend, we can then see what the code setting criteria is for it.