Thanks for the offer Kaz, but I need to stop collecting plants that get big. I got the cutting from achetadomestica, so I feel pretty confident it's White Shatoot. I didn't label well, so a mixup is possible, but I really don't think so. I didn't get mulberries from anyone else. He told me his tree was a rooted cutting, but that all his rooting attempts failed. I rooted it in a pot with a sandy soil mix. I read something about rooting M. nigra, that it's very difficult, but the Persians have a technique where they root it in sand or a sandy mix at a certain time of the year, in winter I think.
The tree has an upright growth habit, mostly lobed leaves (some with 5 or more), distinctive orange cambium, and is a slow grower. It fruited very lightly this year, first year fruiting. Lots of seeds in the fruit. It will be interesting to see what the fruits are like next year. When they started coming in not elongated I thought it was a mislabeled Tice or something, but they ripened white.
I've decided my Thai Dwarf tastes very similar to a VdB fig. When really ripe it has that figgy flavor. Have you tried letting yours continue to ripen?