Klein paradox in the massless case

[Paul159]

I have a question about the Klein paradox in the massless case, for a potential step of height $V_0$ (this is exactly the situation described by Wikipedia). I don't have a problem to understand the "paradox", and I think the Wikipedia's illustration is quite telling.
My question is : what append at the limit case $E_0 = V_0$ ? The "wave function" after the step is constant ($k=0$), and the Dirac equation for the spinor's components $\Psi_1$, $\Psi_2$ become $0 = 0$... Thus there are no conditions for the value of those components. If I choose $\Psi_1 = \Psi_2 = 1$ for example, I still get $T=1$. If I choose $\Psi_1 = -\Psi_2 = 1$, I get $R=1$. I "understand" this with the fact that at the node the group velocity is not defined.
So what would really happen in real life ?

 

[Paul159]

Edit : By continuity of $T(E)$ I would say that the good answer is $T=1$. Also if I end the step potential (I take a potential barrier), the electron coming from the left has to pass the barrier, as it can't change its group velocity. So for me $T$ is always $1$, even in the pathological case $E=V_0$.