Byron
Here is a little code where you put in the 2 heights and u, th at the heights.
It computes the bulk gradient ri, 
ri=9.82/th*(t2-t1)/(u2-u1).^2*(z2-z1);%1-level bulk gradient Ri 
then finds the value of L that is consistent.
It then computes the similarity theory profile of Ri 
Ri=z/L.*ft./fm.^2;%MO similarity ri as function of z/L
and finds the value of z=zr that matches ri.
You can interpret this as the height that corresponds to the value of ri.

It turns out zm=sqrt(z2*z1) is a good approx for zr.  Exact in neutral.

So if you compute ri, you can use zm as z, and estimate z/L .  That gives you u* and t*.

Here I have set t=-0.01 (near neutral).
If you make it -1, you get very stable conditions.

CF