Re: moss on roof
It mgiht be worth trimming hte lower branches of hte trees so you get soem sunlight early i ntejh morning and late in hte afternoon to help dry off both sides of the roof. You wnat shade to teh south, but not always on hte east and west. I'm guessing it's the trees on hte east that are the biggest problem. You mgiht if nothing else thin those out.
You don't want to lose too much shade because it's probably making your summer electric bills a lot sheaper.
1925 Two-Story Stucco Beaux Arts Neoclassical