How did this guy daisy chain the tlc5940 over a long wire?

The great enemy of long wire communications is Line Capacitance and the easy way to counter that effect is to drive more current through the driver, lower the pull-up value from 4K7 to 1K, 470R isn't too much. The net effect of doing this is to lower the impedance seen by the cable and thus begin to provide a better match between the source and the load which is principally the cable capacitance. This is similar to reducing the clock speed. At lower clock rates the capacitive reactance of the cable drops and it isn't as much a load to the source or Arduino. This is also true of really noisy environments too as there is less voltage impressed on the cable by 'stray' electrical noise. I made many 10 meter runs with twisted wire cables... cat 5 sized single pair phone wire at 1MHz speeds.

Bob