Just from briefly looking at the update, I have a couple observations.
I don't know what you've tried yet, but if you haven't already looked into it, you can blend animation over ragdoll in unreal (https://docs.unrealengine.com/5.0/en-US/physics-driven-animation-in-unreal-engine/) by having the bones simulate physics and adjusting the blend weight over time to smoothly transition from animation to ragdoll. You should also look into the joints and joint limits as well on the physics asset to avoid bounces and weird behaviors. Generally the joints are too loose with colliders on the bones able to intersect a lot which can be one way you get those ragdoll bounces and twitchy-ness.
Anyway if you end up with a blend from the current animation to the death animation with a smooth transition to physics you can get some fairly believable reactions without the ragdoll "flop", including when moving as you can have some of the locomotion animation carry over into the death. This is basically what you see in ground branch for example where they animate as they fall and interact with objects. If you want to get fancy you can have different profiles based on where they were hit if you want their leg to give out for example.
You can also do the reverse which may help with the cuffing in some situations, but that's something I haven't tried.
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