You are correct. I don't think I said otherwise. I guess I should have been clearer, time slows down in the frame of reference traveling at c when looking at it from a different frame of reference. I'm sure we are saying the same thing.
>>at the speed of light, all distances in the direction of travel would be zero.
Yeah, but a person observing you in a different frame of reference won't see that. The fact that distances are zero is just another way of saying that time has slowed down in your frame of reference. Is just two faces of the same coin.
Indeed. You can see this sort of effect in, say, the muon decay demo in my relativity simulator:
http://www.refsmmat.com/jsphys/relativity/relativity.html
The muon decay lifetime observations can be explained equally well in terms of time dilation or length contraction.
On the other hand, someone stationary watching you travel near the speed of light would say that your clock slows down more the faster you move, but lengths stay the same.