When you do this stripping of the detergent residue with water softener in the washer, do it with small loads. Did you wash in a liquid detergent? Those are hard to rinse out. Did this just happen with one load of towels? Are you using a new brand of detergent? If they are so hideously loaded with detergent, the small amounts of water in the washer are going to make this job go on forever. You mention the number of rinses, but are the towels getting a very good spin after each rinse? If not, you are just wasting water because so much is held in the towels if they are not spun. If you cannot solve this in the washer, put very warm water in the bathtub and rinse the towels, squeezing them well to force the water through them, maybe buying a new plumbing plunger to use as a washing dolly. In the future, use a good water conditioning product with a reduced amount of detergent when washing.
Since our wonderful & generous member Eddy told me how to program high water level rinses in my Miele W1986, I decided to try once again to wash my bath sheets in it. I use two tablespoons of powder Tide HE and about that same amount of STPP for a load of 3 or 4 of the 36" X 72" bath sheets. They wash well, do not roll up in a ball, fall out to distribute for spin and rinse extremely well with clear, sudsless water in the third rinse. When I take them out, they have a wonderful smell that I can only describe as like very fresh water at a water fall, maybe from the oxygenation. Heavy things like towels get put into the W1918 for a final spin at 1600 rpm which allows them to dry very quickly.