Given a 256 x 256 image of a starspot on a rapid rotator, a starspot looks distinctly not round. It has a eight pointed star-like appearance. Here is the .json file for your perusal.
The level of Healpix pixellation should be set high enough that the spots appear smooth, but not so high that it significantly degrades performance. Try increasing n_side_power to 5 or 6.
Given a 256 x 256 image of a starspot on a rapid rotator, a starspot looks distinctly not round. It has a eight pointed star-like appearance. Here is the .json file for your perusal.