maybe next roof go with a metal one, lot less likely to grow mold/moss on!
BUT if the leaves build up, that where the soil matter is and it will still grow, all the more so if it doesn';t get much sun shine,
LOTS of sun tends to NOT allow the growth! shade on the other hand, seems to make it grow faster!
I wonder how the wood is under them shingles however, all that dampness can ruin it?
best of luck there