Suren put a bunch of info about the work he did this summer on github:

https://github.com/osu-particle-astrophysics/Spherical-Harmonics

He added this in an email:

I added more spherical harmonics into the Chi^2 code so now we can test up to L=12. Adding the additional harmonics brought the chi^2 for the first frequency gain fit down about 30%. However, I also fit the first phase, and it seems to be much harder to fit, especially at the poles. The Chi^2 in in the 200s. Therefore, I am unsure how you wish to proceed with the phases. Perhaps just avoiding the 0 degree and 5 degree theta cones is the way to go. This would involve modifying the chi^2  code and the data to not have those 0 and 5 degree cones.