I've seen people running multi class runs but I've been doing just scout, is there a large cut down of time playing a certain class for certain levels or does scout only work just as fine?

I have a 17:44 multiclass run, it hasn't been approved yet though.

The payload stages are the Scout's best stages, since he pushes the cart noticably faster.

Demoman is great for stages that need a lot of damage, like The Train or vs the Sniper boss.