Stu: I hope the above is not written in a too pointed headed fashion.
That is a nice paper you have linked, but not of much relevance to the the measuring wheel, since we operate in a tiny region at the 0,0 point in the centre of fig1. A tiny force is required to overcome the rolling resistance of our front wheel, and I think it can be ignored.
Incidentally, the magic formula referred to in that paper is well named. It is an experimental equation which fits data which I guess tyre engineers derive from tests on car tyres. I dont think it is derived from a model.
By comparison the formula I have for the NO SLIP CASE is derived from a formula deduced a simple model.