Allow me to use one of Brian Greene's great "Simpson" examples:
Itch and scratchy hop on a train. The train is 1 mile long and drives in a straight line aroudn the earth.
Itchy in the frotn and Sratchy in the back, the train departs from a station.
Homer is in the station and Ned is on the train. A lightbuld in the exact middle goes off.
Itchy and scratchy shoot eachother when the bulb goes on.
Homer says that it was a foul duel because Itchy saw the light later than Scratchy.
Ned claims that they both saw it at the same time.
Who is right? They are both, because light is "client sided".
Well I'm not good at putting these great examples in such a small post, so it might remain confusing and unclear.
You're assuming that light is the limit here.
Also, how is light client sided? How is it possible that it's speed varies based on yours? If that were true then you could never outrun light.
That's the point.
If you were the only one to exist your time would be the only time, but all you are practically changing is your time as viewed by others. If you go faster in time, and people on earht watch you, then they don't go in time along with you. Their time is personal to them. Because light is tightly interwoved with time, as the example above and my post before that, light must result as being client sided too from logic.