There are zinc strips sold for this, they nail at the top . They are
better than copper , but all will work. More sun is the best long
term option, as drying is not now allowed, rot will follow. Trees are
great , but must be trimmed a little. Houses need sun to dry them
out, but mine is covered by 7 old oaks so I understand your
reluctance. Trim a little, I lost my moss problems this way.