A closer look at the join point of the ends of the spiral arms shows a slight tangent mismatch, often less than 2 degrees,
which makes sense, since the join point is not the midpoint between the centers.
You can see the slight irregularity just by looking at the curves.
A comparison between tangents for 100 points versus 1000 points shows an extremely slight difference made by point count.
The 100 point tangent difference was even very slightly better. So the difference is mostly due to the difference in the radii of the spirals.
The Galaxy spirals tangent mismatch just shows up more due to their greater "pitch" change.
The tangents can be manually matched as described above, with the compensation occurring in the center of the spiral.

Taking the derivative of the curves at the end of the spiral arms should enable the compensation to be done by script.
The degrees to rotate is the difference in the arctangents of the tangents.
The derivative of the Galaxy spiral has been calculated.

- Brian