Actually that's not a big deal. Technically you need general relativity to do that, but it's just a quotient space on special relativity. In any case, it works out exactly the same as an infinite series of ladders and garages.
There is one thing you have to be careful about. From the rest frame, the universe could be described as repeating itself every, say, ten feet. But from the point of view of the ladder, it's repeating itself every five feet and 8.8 nanoseconds. That is, if you move five feet, you'll be in the same place, but your clock will be off by 8.8 nanoseconds.
Actually from the point of view of the ladder the universe still repeats at every ten feet. It is just that from it's point of view it takes the space of two carages at any one instant.Both the garage and ladder are in a state of rest and show equally good times. Yes they read different but doesn't mean they are in error.
I am not sure whether it would see other instances of itself. I only spesified a spatial gluing and not that the garage be split into timeslices. I guess that the change of the point of view has changed some of that gluing to be from futur...
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.