Bio powders are supposed to be more effective against stains of animal or plant origin (eg blood, plants stains etc). If one bio powder doesn't agree with you, try another. Does your machine have an extra rinse option? Maybe that will help the skin problem.
I use Lidl Formil Colour (powder) for everything and it's not highly perfumed. I also wash regularly at 60℃ for cottons and 40℃ for synthetics, always choosing very low temperature cycles can lead to smelly washing machines.
Synonymous, I too was pleased to have made my washing machine last many years. However, when it finally had to be replaced this year (17 years old), the new one washes so much better than the old one that I regretted not changing it sooner.