All good points individually Bruce but it's not (or shouldn't be) just a case of fitting wider wheels. The scrub angle can be maintained by varying the wheel diameter and the "assumption" that the force is acting on the centre of the wheel is only valid for static calcs. On cornering the chassis dips or rises, this action moves the point of force, hence active suspension development.
However, when the tyre has almost reached its cornering limit, this concentration point actually moves forward due to the tyre fundamentally changing its behaviour just prior to sliding
I can't say as I understand the "change in behavoir", the tyre is doing exactly as it should, providing a frictional contact with the road. As sideways forces increase so weight transfers through the chassis to provide more down force on the outside wheel, the tyre will deform giving a flat spot that has the effect you describe. As friction is lost the tyre wall re-exerts itself allowing a momentary regain of friction, this is the "warning" that is lost as boy racer drops the tyre profile (lower wall = less deformation = less chance of regaining friction).
Interesting point on varing trail I must have missed a lesson or two. I had always assumed the steering went light as a result of the loss of friction but what you say make things crystal clear.
Does anyone know what the castor angle is on the Beat?
If it ain't broke, take it apart and see how it works