Keegan in 'A History of Warfare' refers to the 'cross-country chariot' (p165 in the paperback version). It "could be driven across rough ground". Chariots of this type were also used for hunting.
On another subject, and totally against my deepest beliefs, I put a fudge factor in the movement system - all tick times required are multiplied by 2.5 in order to allow time for foraging, finding the best route, general disorganization, and so forth. This figure can be reduced for elite troops when we implement that aspect.
This brings the movement rates down near those you wanted.
Cheers.
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