Your rope is moving faster and faster, whether or not it goes all the way around the galaxy. The relations between different bits of the rope are pretty much exactly the setup for Bell's spaceship paradox.
And? The Relativity isn't coherent, that's the whole point.
Transition from one, to another paradox doesn't save the day.
As per a recent comment this thread is meant to voice contrarian opinions, that is anything this community tends not to agree with. Thus I ask you to post your contrarian views and upvote anything you do not agree with based on personal beliefs. Spam and trolling still needs to be downvoted.