  We extend the analysis and discretization of the Kirchhoff-Love plate bending
problem from [T. F\"uhrer, N. Heuer, A.H. Niemi, An ultraweak formulation of
the Kirchhoff-Love plate bending model and DPG approximation, arXiv:1805.07835,
2018] in two aspects. First, we present a well-posed formulation and
quasi-optimal DPG discretization that includes the gradient of the deflection.
Second, we construct Fortin operators that prove the well-posedness and
quasi-optimal convergence of lowest-order discrete schemes with approximated
test functions for both formulations. Our results apply to the case of
non-convex polygonal plates where shear forces can be less than $L_2$-regular.
Numerical results illustrate expected convergence orders.
