The birefringence of BS changed from 17deg to 10 deg after alignment tuning. See the picture for its Jones matrix (Fig1) and birefringence (Fig2). As you can see the JM doesn't have -ve sign any more in the real parts, and is closer to identiy matrix.

The condition on physical realizablity had error bar of 1E-4 (to lower two peaks on BS birefringence).

Polarization ray tracing to correct coordinate systems seems correct. Perhaps can tune BS alignment a bit more.