A user on a different forum wrote a program to compute orbits using my method and the orbits were not closed loops. So the method is correct and it does introduce a precession on its own. The user on the forum used very small step sizes in his program and he said it took his computer hours to make a single orbit. Unfortunately that user quit after a few days and took out the program and the graphs he had uploaded.
I am not sure I understand what errors you're referring to. The summation method, uses the initial velocity v, and the vector g, at position 1 [shown in the drawing] which is obtained by Newton's force law. Then it's just a matter of computing the resultant and using it again at the next parallelogram, shown at 2 and so on. When I use smaller steps, I essentially get the same orbit, only it looks smoother.