> I think we can agree that friction is always opposite to surface speed.
This isn't intuitively obvious to me. One explanation says "must be true", another explanation says "might be false". I'd want to run an experiment with a toy car on a polished surface. Unfortunately, I'm quite a way from the nearest place I could set up such an experiment.
In another words friction slows movement down and does not treat some direction on surface more preferable than others. Assuming regular surface this is pretty much definition of friction.
I am not sure how well I have explained stuff but if you are able to experimentally disprove this it's worth of paper.