Time Travel in Midnight Robber?

After finishing Midnight Robber, I got to thinking. There is a lot of talk about how New Half-Way Tree is in a different dimension. What if instead it was in a different time? I don't know exactly what that adds to the work, but it seems to fit better, and explain current Touissant more fully.
I started thinking about time travel instead of dimensional travel when I first read about the shift pods. While fairly stock, they made it clear that they were not really moving through space. The explanation was that they moved through dimensions, but it seemed far easier to explain that they were moving back in time. I think that New Half-Way Tree is Touissant, but back in time a few hundred years. This makes it more obvious why the myths of the Midnight Robber and Robber Queen spread so easily. They could easily have been already passed on to the people of Touissant when they arrived, and found there way into myth enough that eventually Tan-Tan had the motivation to perform acts of legend. This theory also explains why many of the larger animals are extinct on Touissant, and the Mako Jumbie bird had been domesticated. There is plenty of time to domesticate the bird if New Half-Way Tree is set a few hundred years back. It also explains the absence of the Douen, because they could have been eradicated by the humans of New Half-Way Tree before the colony ships ever arrived, relegating them to myths before the culture of Touissant could exert itself.
However, this explanation is slightly debunked by Hopkinson's own narrative. She does talk about the other dimension a lot throughout the work. Since this is mostly humans talking, there is no problem with just explaining it as human ignorance. However, Hopkinson also talks about Grammy Nanny searching through the dimensions to find Tan-Tan, a description that wouldn't make as much sense if New Half-Way Tree was just back in time. The time difference though does explain why Grammy Nanny cannot affect anything that happens on New Half-Way tree. Grammy Nanny would not be able to affect anything before she was created. This would make the scene with the shift pods more believable too, because the eshu kept talking to Tan-Tan for a reasonable length of time while in the shift pod. If the shift pod was traveling back in time, then the eshu would have a reasonable amount of time before the pod went to a time before it was created.
Still, in the end, time travel doesn't seem all that likely. There is only one reason why Hopkinson would state that it was dimensional travel instead of time travel; to show an interesting recursive myth creation that would not add all that much to the story, and create weird paradoxes. If the myths that Tan-Tan was told were about her it would create a lot of pre-determinism that doesn't really fit into the story. I like to think that the time travel works, but it doesn't add enough to the story to justify me shoehorning it into Hopkinson's work.