Ilford probably made a compromise between all the variaions out there and provided a standard method.
However shaking the water about makes little difference to the rate of diffusion as long as the water moves over the surface from time to time. Certainy the temperature of the water has a greater affect. And if very cold the total time should be extended.
Thin emulsions should exhaust quicker than thick ones everthing else being equal.
The original Ilford manual of photography, the focal encyclopedia of phothography, and the Kodak data sheets, all gave variations on the theme.