I wish I had the answer. Our pigs love fleece too but we never got around the hay in the washing machine problem either. We use their blankets to make a tent for them at night which they love. They are indoor pigs but they have animal hot water bottles at night too.
Our guineas live on fleece, I wash it inside an old duvet cover that I have sewed a drawstring around the top of. I give it a good shake in the gareden before I wash it though and I vacuum the inside of the machine after the wash to catch any stray bits.