Are your suds lively enough?
For a nice thick type of suds, nothing beats plain soap. Try grating a bar of Ivory, adding about 1/4 cup of STPP to the wash first, then the hot water, then the soap. For more suds, add more soap. Easy!
As the vintage Bendix owner's manual advises, you want "lively suds", which with soap are best obtained with a good non-precipitating water softener like STPP.
3-5 grains is not overly soft water. The water her runs around that but it can still leave mineral spots and deposits on glassware. A good example is the drip tray on the fridge water dispenser. It's black, so it shows up the mineral deposits very easily. And they do accumulate if the tray is not wiped dry after any dribbles or drips on it.
In other words, STPP or other non-precipitating water softener (like zeolites) will help the soap build and maintain a nice thick layer of "lively suds".