Actually, in terms of moving current along a conductor, they move astonishingly slowly.
I did some sample calculations a while back and I know that copying and pasting from a spreadsheet doesn't format well but here goes anyway:
I 1000 A
PI 3.142
r 18 mm
A 1017.87602 mm^2
Q 8.5E+19 per mm^3
e 1.6E-19
v
0.072238082 mm/sec
Worked better than I expected...

This for copper.
Note the v. And the units.
I'm sure, since you are an erudite chappie, you will know of the train and tunnel analogy so you will doubtless excuse my indolence in not typing it out here.