Not sure what I'm hearing exactly... The heat shield rattling or maybe ACCT noise.
Explain to me what's going on with the left handlebar around 1:20 of the first video. Looks like the bar is broken and the cables on both sides are heaving up and down? I installed my damper gear 180° off by mistake, I couldn't see the handgrips because they shook that bad. Can't say for sure but you may need damper bushings if nothing else is causing the bar noodling.
My bike has new dampers, runs smooth as possible ... I have some saddlebag tethers on the license plate, and one of those will shake at idle, much like that loose heat shield is doing.
Sounds like it's running ok, rev hang didn't seem real bad, but it did react slightly when you sprayed it. So maybe a small air leak.
The gray smoke is a rich mixture, same with black plugs.
The heat shield is loose, so possibly that came out better in the audio than the motor.
The camera very poorly captured it, it was vibrating hard, and it took a while for the bike to calm down and stop shaking like that. Honestly, it seemed as if it had to be fully warmed up before it would run half decently. I did bend the forks & handlebars, so bushings might be included in the repair.
What's the best way to tune the carbs? I figured I'd at least start there. Guessing also plugs might help?
The gray smoke stopped after a while, I'm guess the cylinder got flooded from multiple failed cranks, so it finally burned everything off.
Far as air leak, I'll have to look at the carb again, see what I can find. Again I'm not sure how these things are supposed to idle naturally but, it definitely doesn't seem right/seems way more erratic than it was before the crash.
I did not look at the cables, I will have to do that.