I apologize in advance for the wording. Human languages - and most especially English, or so it seems - are not very good with time. If you understand what I've written but can think of a better way to say it please mention it.
Now, I am neither a Physicist nor a Philosopher, but...
Of the various models of time, many seem to require that there be some existence that extends beyond the instantaneous 'now.' Time in those models is a place that has reality outside of now, such that it may in principal be possible to alter one's location in time to visit either the past or the future or both, depending on the particular model.
If time is in fact a continuum, with past and/or present being simply locations along that continuum, then it seems that one's rate of experience of duration should necessarily relate to movement through the time dimension. To experience one second of duration is to advance one second along the line of time, just as advancing one meter in a particular direction is to move to a new location one meter removed from the previous point along some arbitrary spatial axis.
In the physical dimensions traveling between two points requires the same magnitude of physical movement regardless of the rate at which that movement occurs. By analogy, travel between two points in time requires the same magnitude of duration regardless of the 'rate' at which that duration occurs.
Given that objects that experience different degrees of time dilation can travel between temporal locations without passing through the same duration, does the existence of time dilation imply that the temporal continuum does not in fact exist?
Presentism does not seem to be in conflict with time dilation - the passage of time is a measure of the rate (for want of a better word) at which one experiences duration relative to others in different frames of reference.
So... does time dilation demonstrate that models of time that treat it as a continuum are flawed or have I missed something in my line of thought?