I'll echo what many have said already, but I'll also say that rebuilt hundreds - maybe even over a thousand coaster brake hubs, and I've never heard of this problem before. I'll be very interested in learning what it is.
On grease: Park grease is good grease, but in my opinion it is best used for assembly, and not for bearings. Any non-moly marine grease will work so much better for the extreme pressures encountered in a coaster brake.