Well, not knowing the relativistic equations that provide the numbers, speculations and fat chewing are my specialties.

Why indeed would it 'seem' to slow down (time, that is).

I would have to revert back to how I define the human term, "Time" to answer this one IMHO.

Travelling at c=mc^2, the number of discernable events decrease from observation, in contrary to the number of events increasing from travel itself. For example, riding this beam of light, passing by a nearby star, a decrease in observational events are noticed from the star, but passing the star speeds up thus increasing the number if events of passing objects.

This would seem to me, that the micro universe slows down, while the macro universe speeds up. Inversely, travelling at zero velocity as a human observer, the macro universe slows down, and the micro universe speeds up.

Relevant analogies would be the movies "Honey I Shrunk the Kids!" to represent the macro universe slowing down, while speeding up the observable mico universe.

Granted, no matter how fast you travel, the speed-up/slow-down is only perceived, not actuality.

-Tchzarmok