It turns out that SciPy's Fresnel values are wrong for complex arguments and large enough absolute value. I'm trying to fix that.
The implementation is based on Zhang/Jin, Computation of special functions, which in turn is based on Abramowitz/Stegun, Handbook of Mathematical Functions. There we find for the Fresnel S integral (7.3.10) $$ S(z) = \frac{1}{2} - f(z) \cos\left(\frac{\pi}{2} z^2\right) - g(z) \sin\left(\frac{\pi}{2} z^2\right) $$ for all $z$ with the auxiliary functions (7.3.5), (7.3.6) $$ \begin{split} f(z) &= \left[\frac{1}{2} - S(z) \right] \cos\left(\frac{\pi}{2} z^2\right) - \left[\frac{1}{2} - C(z) \right] \sin\left(\frac{\pi}{2} z^2\right),\\ g(z) &= \left[\frac{1}{2} - C(z) \right] \cos\left(\frac{\pi}{2} z^2\right) + \left[\frac{1}{2} - S(z) \right] \sin\left(\frac{\pi}{2} z^2\right). \end{split} $$
Computation of $S$ for large values is done via the asymptotic expansion of $f$ (7.3.27) $$ \DeclareMathOperator\arg{arg} \pi z f(z)\sim 1 + \sum_{m=1}^\infty (-1)^m \frac{1\cdot 3\cdot\cdots \cdot (4m-1)}{(\pi z^2)^{2m}}, \quad z\to\infty, |\arg(z)|<\frac{\pi}{2}. $$ This is where I have problems understanding the approximation. Consider $f(iz)$; for the asymptotic $f_a$, we have $f_a(iz) = -if_a(z)$. However no such thing is true for $f$ itself. Numerical computation via the representations $$ \DeclareMathOperator\erf{erf} \begin{split} S(z) &= \frac{1 + i}{4} \left[\erf\left(\frac{1 + i}{2} \sqrt{\pi} z\right) - i \erf\left(\frac{1 - i}{2} \sqrt{\pi} z\right)\right]\\ C(z) &= \frac{1 - i}{4} \left[\erf\left(\frac{1 + i}{2} \sqrt{\pi} z\right) + i \erf\left(\frac{1 - i}{2} \sqrt{\pi} z\right)\right] \end{split} $$ shows that the approximation incorrect for everything off of the real axis, but the issue here could be numerical instability in the $\erf$ represenation too.
My current guess is that the above infinite sum is valid only in the area $|\arg{z}|<\pi/4$, which would already change how we compute the Fresnel integral values significantly.
To finish things off, here's a cplot of $f$ (for smaller $|z|$):