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Not trying to insult your intelligence or anything, but try to avoid close curves, jump too much, bumping into things ahead of you, walking on ice (not the snow, of course), etc. Also, don't worry about collecting the items that give the time bonus, there's more than enough time to finish the race.
Since you probably already do that stuff, reconnect the controller, check if it's not dusty or anything, check other games to see if the problem continues.
You already covered pretty much everything to win the race, so there's not much I can say. Your only problem seems to be the running speed, possibly due to the con-troller. Get a new one eventually or borrow one from a friend. I don't know about you, but when I try to repair something by myself, they usually end up permanently broken/get worse than before, so I don't advise it.
Either that, or Ammy is getting old... even divinities get rusty after a 100 years hibernating.