Looks like going to be this type.

So far as encouraging a switch back to fruitful productiveness... I don't know - unless you do something to damage it in a non-lethal manner. Have seen non-productive, senescent trees of numerous species that put forth a heavy crop following HARD pruning, or being subjected to hurricane-force winds that came close to toppling them(while also toppling some of their contemporaries).
Or, you could, as some old-timers might offer, beat it with a mallet.

You can see (barely, I apologize for the poor quality of the image) in the pic of my 'Black Beauty' Morus nigra, which is probably not as far along as yours, having just popped leaves a few days ago, that the flower clusters are already present (just below the largest leaves at center).

Lucky is probably right about the switched gender... I hope it is not permanent.

First, a female just leafing out... Notice that you can already make out the size/shape of the mulberries to be, even though what you are looking at are actually aggregates of flower buds and/or opened flowers!

You can easily confirm the sex of the flowers when they open with the aide of a magnifying glass (just compare to online images of staminate and pistillate flowers of Morus).

Hope this helps...

Re lucky's advice about a shock: I'm thinking about pruning it hard next winter, in spite of all the literature advice being not to do so after a certain age for morus nigra. There's nothing to lose since I don't need a non-fruiting mulberry, but I would like to be judicious about it for the best chance for success. Any ideas about how hard to prune or what diam. branch at which to stop? Do you know of other ways to shock the tree into another gender change? Gross feeding?

Re fabaceae: you're right about my being wrong about the timing. The aberrant tree has 2 female flowers on it among the hundreds of male ones right now. As well, our other, younger, morus nigra has loads of female flowers this year, hooray.
Hope we get some ripe ones before the birds this summer. I used to erect a tent of tall poles with balls on top to net the tree. What a palaver.

Morus nigra varieties are self-fertile which means that a lone tree will form fruit (seedless) without having any male flowers on it or anywhere in the vicinity. Most wild Morus species need to be cross pollinated (by the wind blowing pollen from male flowers on one tree to the female ones on a different tree) in order to form fruit.

Late this winter I grafted onto it scion from lavender mulberry, pakistan white & early white - obviously female.

The early white came in early with a cluster of the biggest mulberries I've ever seen. The lavender are just about ripe now. Nothing from the Pakistan, which hasn't put out a lot of growth yet, but looks like a healthy enough take on the graft.

I'll be looking to add more varieties this coming winter/spring.

So, if your tree really has gone over, find some scion wood and graft, baby graft. Maybe combine grafting along with the hard pruning, as suggested. Even if the shock tactics don't cause it to gender bend again, the grafts should take off with vigor.