what kind of tapwater do you have?
riccia is a fastgrower as well, but it needs access to all micro's and makros..
even the ones we don't really supply..
Growing Riccia commercially, I have an advantage of monthly water reports etc. and if I find a drop in one nutrient, the Riccia will have responded equally.

Riccia NEVER attaches itself.. it might get stuck to something, but it won't stay there..
Riccia can grow underwater stuck in javamoss, driftwood, eleocharis etc. but now of it's own accord.
Tying it with fishing line is fine.
An easier way would be to use hairnet. that way you have a better hold on more mass, than when you tie it.. you need a lot of fishingline to have the same hold.