Is this a good idea and do you think it will work? Worth the $1,200? My only hesitation at this point is asking the friend and they go through the hassle but then it goes sideways and still do not gain access to my account.
I think it's not worth it even if you do the KYC they'll still ignore your request at all considering you're from USA and their T&C wasn't allow such citizen. It's a worthless initiative I guess even if you pass a KYC. If somehow you can ask some friends that doesn't care on their privacy and information as well then I guess you'll still be in luck. That amount may not be huge for a US citizen I guess, it's your call if you want to do the necessary things.
If that happened in my case, I will comply with the KYC since I'm not really concerned about these identity-related issues if the involved site is somehow reputable. But since OP stated that even complying with KYC won't clear this mess, then it will change my view that why should I still submit if there will be no good outcome later on.
That being said, OP should now try everything if the eagerness to get the amount is really important. While at the same time, OP should now slowly accepts that the issue might not be resolved.