I thought there are only three classes of infantry in terms of move speeds just like there are only three classes of cavalry (fast, normal and slow)? I would have thought these three classes differ in both walk and run speeds. I think your running speed categories may identify the three classes, but are you really sure there is a "very slow class" which comprises only DGK?

Special formations like shield walls, phalanxes etc may have additional effects, but that's a separate issues.