I have tried paper mulberries in a few different places in the world and tried my first ones in paraguey when I didnt know what they were and again in vietnam. There isnt much flesh on them, but the flesh they do have taste alot like a fig if you turned it inside out, with the flesh being very soft. There also seems to be some variability between trees with some trees producing more than others. I collected seeds in Vietnam, but found out from literature they they can be very invasive, so I didnt bring them in. On my family's farm we have many old male trees and they sucker up all over the place but look really cool. The trees are over 80 years old and are covered in knoppy growths. Birds can spread them very easily too. I did like them a bit and as said I have male suckers all over the place and in the future wouldn't mind a scion to grow, I'll just to graft it onto a sucker and keep it in greenhouse so that none of the seeds could get outside. Males produce a lot of pollen and can cause seasonal allergies. Also there are many many varieties of mulberries here in china and I am sure that most of them are only here in china. I read a paper a while back and it talked about 10 or so species of mulberries being native including several morus macroura being huge. There was a species with even longer fruits that were loose and looked very similar to catkins and not a blackberry.
BTW does anyone grow Morus rubra? Are there any improved varieties? I have several different M negra, M alba, and M macroura but have never seen or tried the only one that is native to the states. There are also many other species of mulberries out there too like M texanas and lots of other asian sp.