100% user error in my opinion. You must determine what actions you physically engaged in that caused these bans to occur. Once you know the actions involved you can reduce your risk exposure points. You absolutely must go back to the basics here and research possible reasons your domains are getting banned. There are dozens of workarounds for posting domains to social networks, and many of them will work for you, but none until you figure out what you did that caused this to occur.
In my opinion your posting mechanism is highly suspect in this scenario and the most likely culprit to have exposed some portion of your project details - most likely an IP address associated with your poster engaging in posting your link across multiple accounts. Extend Twitter the courtesy of their tech saavy workforce. You must be working smarter than many of the smartest coders in the industry. Your project is stalled and bottlenecked, so don't look for a quick fix or you will be back next week asking why your new domain is banned again.
Now seriously OP - WHY is your domain being banned? You would do well to separate your issue with Twitter from the mylikes.com situation as your domain being banned is likely not too closely related to the redirects. Admittedly it is a possibility, but absolutely incorrectly posting the links to Twitter is a more likely scenario that would result in domain banning.
Also the more I think about it the more likely it seems you may have actually posted the links to the SAME twitter account which got the original domain banned. Now just think about that. That occurs to me because you aren't complaining about accounts getting banned - just the domains. You didn't seriously post the new domain to the same compromised account OP, right?