Not necessarily pause squats... it's just that those dive-bomb squats put a ton of pressure and damage on your connective tissues, and these connective tissues don't recover as fast as the muscles (they have less vascularization, so they recover harder).
Overtime, they get too damaged.
That's why as Kingfish does squats daily or so, he can't afford that damage. That's the reason for his paused squats (among others).
In your case, just be more solid on the eccentric phase.
Hey, nicely done. Yeah, in the 2-leg bounds I get a lot of quad load as well, and also a "very positive" shin angle. So it definitely looks really quad dominant. But at the take-off point, you still have to push those hips forward with power, and that's paramount. Just don't go overboard.
I can relate to that double-bounce on the landings. It happens to me when I do 2-leg bounds for length while barefooted. It seems that it's a strength issue for me, and I let the passive elements take in the shock and "bounce" on every landing.
If anything, try to be smooth, don't CRASH, even if it means you're going to go shorter distances.
It's nice that on the speed bounds you did better, so you're capable of it.
Keep doing what you're doing and consider getting a kettlebell. It's about ~100$ here in Romania, at 24 kg, and you will have it for your entire life if you don't drop it or something.
For the donkey ankle bounces, you should be extremely quick and WITHOUT loud noises:
Then you don't have enough "strength" IMO. You should use a slower descent and less weight. Safer, and more time under tension.
Use a faster descent on more specific stuff like half squats, and even then, you can do Lance's quick dip only in that specific range of the amortization phase.
It's impossible for me to run in parks, with tens of dogs with no leash or mouthguard jumping on you every time you run. It's so retarded. And I'm talking about dangerous dogs. I hate dog owners that think their dog is "special" and "won't bite you".
That's like me point a gun to your head and saying "oh don't worry, the safety is on". Well how about not pointing a gun to my head to begin with?