Put in soil and let it cycle between wet and dry, this means its supose to be 75% time wet soil 25% time dry soil.
When its wet she picks up size and water, when its dry she expands root looking for wet soil. If it has been always in wet paper place in soil but only spray the soil lightly don't make it too wet to the point where it takes 3 days to dry.
Hey Mate,
Maybe you should have planted it into your Medium as soon as the tap-root showed itself...
Don't know if she grows any further, but surely not between two papertowels...
Good luck mate!
Cheerz
OimRausch