So, I also own a ‘90 Jeep YJ... it had a slight tick at startup that went away once it warmed up back in ‘09. Figured since it drove I wasn’t going to mess with it. Fast forward to 2016, and I start it up one Saturday morning... it sounded very similar to what your hearing. Mind you this is without any change from the previous sound. My diagnosis back in ‘09 was I had a lifter that wasn’t cooperating until warmer, thinner oil tried to intervene.
It was at that moment on that Saturday morning I thought it would be a good to pull the motor for a rebuild it’s been needing. What I found when I pulled the head was a lifter (remember the one I spoke of earlier?) stuck in the lifter valley. After removing all the others this particular one was seized in place. Obviously, if it can’t move the cam is eating both itself, and the lifter. Yeah, kinda sounded like those videos.
Another thing that makes me think the lifter is because of the frequency of the knock/ noise. It comes around very often. Think of the small circumference of a lifter... doesn’t take long for the high side of the lobe to come around and strike.
Hopefully... I am way off. Hopefully... you get this resolved with no major work. As to the question you ask referencing driving until it blows up, or getting it repaired... I’m kinda leaning on driving/ towing it to the dealer and complaining about it. Not sure I could bring myself to drive it until it blew up... unless of course they document they saw nothing wrong. Which we know would be insane. The dealer that’s been doing the oil changes should have definitely brought it to your attention.
Good luck. Keep us posted.