Time is just the sequence of events. And events on the smallest scale are particle interactions.
What if there is an unknown quantum field which creates a barrier between particles? And particles have to "tunnel" through it in order to interact?
When this quantum field is more disturbed (warped, etc) this barrier will be greater and it would be harder to particles to interact with each other. The end result is "time" slows down since the number of interactions drops.
Note that an observer (in its own reference frame) will not notice anything (in the same way as in general relativity) since the observer just counts the number of interactions. To that observer the same number of interactions means the same amount of "time" passes.
And yes, this means this quantum field would be a distinguished reference frame.