I was about to say, my Cabrio XL does a saturation lather on a number of cycles...it starts with a slow spin to saturate the load, and then a high spin to pull it through the items...usually 3 or 4 times....then filling continues and wash begins...
also with this machine if you watch closely, no matter what you select, the softener will flush/dispense, and the sprinkler comes on and recirculates rinse water over the load as a spin spray, using minimal water......but if you select the 'softener' option, it will fill for a deep rinse....if you select 'extra rinse', it will do a spin/spray and a deep rinse
the Calypso does a similar saturation spray at the beginning of all cycles...
in thinking about it, Tom's method would work really well for pillows, as some can get distorted from tumbling or agitation....a series of sprays and soaks, then on to a few rinses the same way...and a final spin...