Two cables, same resistance, different lengths, speed of current transfer
Your model describes a short, highly resistive cable where the resistance dominates the cable inductance and capacitance. Such a cable will have such high attenuation that you would never observe signal propagation over very long distances, so the signal speed never becomes an issue.

A long, low-loss cable is well modeled as a series of short segments. The model for each segment of cable is a passive network that accounts for the resistance, inductance, and capacitance within the segment. For a given input signal, one has to solve the entire network of segments in order to find the output vs. time. 

Fortunately this was all worked out >100 years ago: http://en.wikipedia.org/wiki/Transmission_line. Basically, one keeps dividing the (fixed-length) cable into ever shorter segments. In the limit of infinitely many, infinitely short, segments, one obtains the telegrapher's equations (see the Wiki article).