Analysis work by Pierre Astier suggests that the common failures to fit the ConstrainedPhotometryModel in HSC are due to excessive outlier rejection of stars with beyond median color. To fix this we likely need to implement a focal plane color term as a fittable object, to correct for the color variation. For now it can be a constant across the focal plane or constant per-visit, but it should allow for position dependence, and will have to provide parameter derivatives for the fitter.
Pierre is also investigating algebraic methods to identify outlier stars whose removal may cause the problem to become underconstrained. Progress on that may result in this becoming less critical.