I am also not a professional. However...
The paper describes the time dimension heading toward a singularity. So, we'll get the universe rapidly expanding outward faster and faster. However, there will be a point at which there is a "big freeze", where time will stop. However, there is no 'experience' of time stopping. Instead, we would experience time as normal as we are attached to it, and would have no clue that we can go no further. There is a very interesting description of this in "Einstein's Dreams".
So, putting it into your explaination, all that spaghetti rotating in the forth dimension would keep doing so. Only an observer *outside* of time could ever see the change in the brane-space and only they would ever see the stuck versions of ourselves at the point of the signature change.