How do we model the behaviour of circuits on ultrashort time scales (< ns)?
The guy you seek advice from is Maxwell, not Kirchhoff.

If you want to use circuit theory and its variables like voltage and current (and Kirchhoff's Laws are about voltages and currents), the overall dimension of your circuit d must be way smaller than the signal's wavelength, which is clearly not given if your thought experiment is about the LEDs flashing along the wire, one after each other. In that case, one would have to use field theory (with electric and magnetic fields). You still can integrate over all relevant elements within a given sphere and find out that sums become zero, but that's Maxwell, not Kirchhoff.

Here's an excerpt from Chua, L. O., C. A. Desoer, E. S. Kuh: Linear and Nonlinear Circuits. McGraw-Hill Book Company, New York 1987, ISBN 0-07-010898-6, p1-3; online (in part) at http://www-inst.eecs.berkeley.edu/~ee100/fa08/lectures/EE100supplementary_notes_2.pdf.



The fact that this is on the first three pages of a > 800 pages book about circuit theory, put almost as a disclaimer in the first chapter, called "Kirchhoff's Laws", kind of speaks of itself.