Beat me to it, I was going to say just this.Dealing with Jeeps for most of my life and I have installed lockers of various styles. None of them would be damaged by Mot brake tests or rolling roads.
If you do remove the LSD or ring carrier and change bearings you just need to make sure the backlash is correct after installation. A magnetic base and dial gauge make this easy. I am not sure if the BMW cases are adjusted with shims or adjustable preload nuts.
I have built a lot of diffs and as long as you understand the settings and have access to the tools they are not difficult.
Anyone can find alot of information from Randys ring and pinion, A US company that specializes in different diffs.
Reading it all makes it look complicated but there is a lot of very good information that can be transferred to any rear end.
https://www.randysworldwide.com/resource-center/?fwp_resource_center_categories=gears
The Z3 diff preload is done with that crush washer, easy to do with the torque angle gauge 25nm of load if my memory serves me well. The LSD unit is done with shims either side you'll need some engineers blue to know that the teeth are meshing central. That first video you listed is the guide I followed.