I realized just today that I probably left out the one period study that speaks directly and in detail to the question of movement rates:
General Jarry Treatise on the Marches and Movements of Armies translated by R. Rochfort 1807 97 pages Jarry was a French Officer who was hired by the Prussians to run their military schools before the Revolution. Around 1800, he left Prussian service and worked with the British to establish their military academy. I believe the work is available through Archive.
He also wrote what is probably the most comprehensive work on light infantry tactics before 1810.