I notice that on Hanto as a Japanese, I barely percieve any problems with Classic run speed. That's partially why I'd guess the exhausted sprint speed is the problem, because on Hanto, you're often running from cover to cover in short spurts--you never exhaust your stamina bar, and so the movement feels and looks natural and smooth.
On a map like Guadalcanal, though, as a Japanese, or on Saipan as an American, you're often running long distances, and that's when you feel that you're running far too slowly... because you've depleted your stamina bar and are moving at what basically amounts to a jog.
Next time you play Classic, try and be a little aware--when is the slow sprint the most noticeable? At what point do you think to yourself "I really feel like an eighty-year-old right now..."? I'll wager that it's when you're already exhausted, running on an empty stamina bar.