Another 301 that doesn't have the problem and I never fiddle with my tension. I also don't worry about thread weight - just color and sheen. Even thread painting the eagle and ducks on my son's quilt, no thread showed on the top or bottom.
But that being said, with another machine, I'd make a quilt sandwich of the same fabric and batting and play with the tension - both the top and the bottom. There has to be a sweet spot, IMO.