Great submission thanks. The tree structure you use is very efficient.
I compared, as you did, the accuracy of your implementation with the results reported in M. Sabry Hassouna et al. "Multistencils Fast Marching Methods: A Highly Accurate Solution to the Eikonal Equation on Cartesian Domains". Not sure exactly what they do but I found that the accuracy depends a lot on how the results of the two stencils are combined (which is somewhat arbitrary since we do not know a priori which stencil provides the most accurate result).
To improve the accuracy here is the trick: instead of computing the distance with the first and second stencils separately, simply sum the corresponding second order polynomials and solve the resulting second order equation. In other words, simply replace