I don't prefer really long bows, so if I had a 31+" draw length and wanted to shoot a longbow, I would personally go with a 56" Shrew Classic Hunter that would be a pleasure to carry out in the field hunting elk and deer. With your background in shooting compound bows with their short lengths, you may have some real problems adjusting to a 70" bow or something similar. BobW here on TG has a 32+" draw and shoots a 56" Shrew CH with no problem. If you don't mind carrying a bow that is almost as tall as you are, the bows that others have mentioned would probably work fine.
Allan