That isn't possible. Time is as part of space as the other dimensions. Time is distorted by mass, just like space.

You can't move "purely on the Y axis" any more than you can move "purely on the time axis", or vice versa.

Off topic: Why is it a new idea that the observed motion of the universe around us is affected by "faster time" in denser areas of space? Why is that not blindingly obvious? Bwuh?