Cleaning the coolant bottle is important also. First I tried purple power (caustic) with aquarium gravel to help scrub when shaken. Little improvement. Next I sprayed some aerosol engine degreaser (petroleum product), added a handful of oil absorb (think kitty litter) and shook. Excellent results! My only dislike was the residual petrochemical odor on my clothes.
Wish I had taken some before photos, but here are the afters:
Coolant bottle2.JPG
Coolant bottle1.JPG