If your pit is too close to the surface, the ground could be frozen and not perc in winter. High water table also slows the perc rate. Then the pit stays filled up for a long time and the drains connected to it back up.
Is a larger pit feasible? Just so more water can be held and you can do more washloads in a row before the pit overflows. (You'll still have to wait until the water soaks into the ground.)
When cleaning anything including baby diapers, it is better to sweep off or scrape off as much solid and semisolid material as you can first. (1) Less cleaning fluid or detergent needs to be used, (2) Less of a mushy mess which in turn means that bleaches or disinfectants will be more effective.