Here is an example, where time dilation is coordinate-independent. Alice freely falls into the rotating BH. When she crosses the second horizon, she stops and hovers (enjoying the spectacular view of the naked ring singularity). As ring actually repels in some places, she would be safe and probably can even switch off her engines. Bob waits 1 day, or 1 year, and does the same. How long Alice would wait his arrival? Note: as BH is rotating, when Bob arrives Alice can be on the opposite side of BH, so we look at the scenarios where Bob is lucky, or 'in sync' with the rotation, so they meet.