First of all washing machines` rinsing efficiancy is usually determined by residual alkalinity, not froth. Of course if intermediate spins are affected by froth, rinsing efficiancy degrades, but:
Cotton is very absorbant and nearly impossible to rinse bubble free and cristal clear in a frontloader because even the smallest amounts of man made surfactants whip up froth. This does`t necessarily mean the clothes are not sufficiantly rinsed.
On the other hand synthetics are less absorbant and in particular polyester has a tendency to attract grease so no bubbles in the last rinse might even indicate not compleatly clean.
Soap as has been mentioned already is most difficult to rinse out even if the water looks perfectly clear.
As to stiff clothes, do you live in a hard water area? Constant underdosing of detergents leads to calcium build up on clothes which is unfortunately irreversible. If you want to cut back on detergent I would use a seperate water softener not for the washer`s sake but for the clothes`.
Have to say when I was young I was obsessed with rinsing as well. I only used half the recommended dose of detergent and have always reset the timer to some extra rinses because of the foam. Had problems with stiff clothes as well.
Today I use the recommended dose of detergent, hit the extra rinse- water plus button and let the machine do it`s thing. Honestly never had a skin reaction because of the foam and no more stiff clothes.
I would also like to share another observation with my fellow Sudsophobes here ;-)
If you use Listerine after brushing your teeth you are supposed to spit only, right ?
Sometimes I follow a clear water rinse and guess what, the surfactants foam up like crazy in the rinse with water, even more than when squishing the undilluted product around and I`m still alive.