I managed to exclude the Helmert transformation parameters by a special preliminary coordinate transformation:

1. translation to the center of mass

2. scaling (the largest distance from one of the points to the center of coordinates is 1)

3. rotation (the point that is farthest from the center of coordinates lies on one of the axes).

The search for the values ​​of the remaining four parameters is carried out without problems. With this approach, you need to understand that the deviation of the farthest point has the greatest impact on the result. My code is still terrible and unreadable and it is too early to post it, but I hope the main idea is clear