Crossed version: the two photon emissions are swapped.
The computational chain
From diagram to number—every step of the amplitude calculation.
The diagram
The photon emission order is reversed compared to the t-channel: the electron first emits photon $q_2$, propagates as a virtual electron with momentum $k = p - q_2$, then annihilates with the positron to emit photon $q_1$. The propagator denominator is $k^2 - m^2 = u - m^2$.
Feynman rules expression
$$i\mathcal{M}_u = (-ie)^2\,\epsilon_\mu^*(q_1)\epsilon_\nu^*(q_2)\,\bar{v}(p')\gamma^\mu\frac{i(\not{p}-\not{q}_2+m)}{(p-q_2)^2-m^2}\gamma^\nu u(p)$$
This is the t-channel expression with $q_1 \leftrightarrow q_2$, which replaces the virtual electron momentum $p - q_1$ with $p - q_2$ and swaps the Lorentz indices on the polarization vectors. The gamma matrices appear in the reversed order along the fermion line compared to the t-channel.
Squared amplitude (u-channel alone)
$$\overline{|\mathcal{M}_u|^2} \supset -2e^4\frac{m^2 - s}{m^2 - u}$$
The trace structure is identical to the t-channel with $t \leftrightarrow u$. Where the t-channel gave $-(m^2-s)/(m^2-t)$, this gives $-(m^2-s)/(m^2-u)$. As in the t-channel, the positron completeness relation contributes $(\not{p}'-m)$ with the characteristic sign flip relative to electron spinors.
Mass dependence
$$\text{Denominator: } (m^2 - u)$$
The propagator denominator $(m^2 - u)$ vanishes in the massless limit. The electron mass is essential and cannot be neglected.