Tom,
If the tyres have done some miles I would swap the front left with the rear left, test drive then swap the right hand side front and back and test drive again, then assess what happens. I have had some really strange wheel effects if changing sides and thus rotational direction. No, I can't explain how a tyre with one direction of use that is then reversed can do this except perhaps with directional tyres but they do! However do check that your tyres do or don't have a directional arrow or an outside marking!
