Poorman's shunt theory
A is not surface area it is cross-sectional area. 

So L = \$\frac {A R}{\rho}\$ = 0.291m 

A  = 2.5E-6 m^2

R  = 0.002\$\Omega\$ 

\$\rho\$ = 1.72E-8 \$\Omega\$ m (your number)

You're right, it's a lot easier (from first principles) using European units rather than gauges, but usually we just look it up in a table. 

Copper has a quite high temperature coefficient  (about +4000 ppm/K) so it's only useful as a crude shunt. Even brass is better, but nichrome constantan or manganin would best (in order of possible difficulty to source).