If oxi/bleach did not work, I agree, the duvet cover is the answer. If you cannot find a reasonable one, then sew 2 flat sheet together like a pillowcase. This is easy & inexpensive.
Try aplying lemon juice to the stains and put it in the sun. Then bring it in and wash with Tide and vinegar and bleach. First put bleach and tide and then vinegar. Do not put in dryer as it will seal the stains.
I've used bleach and dishwater detergent in the washing machine with great results.I usually pour it in, run hot water and let soak over night. Good luck!
Also thought about cutting apart and using for large pillows, seat cushions, bench cushions...need to learn how to sew. lol