@alex717,
To be honest, such things are dependent on definitions. I always go back to definitions, because in Philosophy most arguments arise from two people using words that are the same with different meanings.
Time, I would argue, is an organization of movement and change in the human mind. Therefore, for "time" to be infinite, the universe should be infinite in one way or another. If the universe is infinite in potential space, then movement in one direction would be a constant for time to exist infinitely.
However, the idea of time overlapping is intriguing, as it would require all things to move in the same exact was as before. That is, if you take Time in the definition I gave.
If the universe is all there is, then,
given an infinite amount of time,
it is entirely possible that reality could move in the same way it is currently moving, but after these movements have finished.
(I bolded and italicized those on purpose, because the implications of what you say in regards to this topic are not short of applying in every aspect of your philosophy.)