If we get to that point, it will probably prompt me to knock on the neighbors door to ask about the trees 
But I have enough trees at better sites that I’m mostly curious about what this will do. And a few jujube to snack on while I mow is always nice.
The Honey Jar seems to have much more fruit than in the past, but that could be due to the excessive sun so far this year. And just over the last week or so since I posted, I’ve noticed more on most of the trees- 1-2 becomes 6-10 and the HJ and SC have decent amounts. Just the Li is the barren laggard.
I’ve got a couple possibilities about the declining productivity of your shaded jujubes.
1.) Self-shading, as they get bigger (already short on sun, it gets worse when there are more branches)
2.) Bigger roots
a.) result in more and faster growth. Growth distracts jujubes from fruiting, which is why snipping vertical leaders (like pinching figs) promotes set
b.) I’m not sure if periodic dryness is needed, or if it just helps tamp
down growth (as in 2a). But big roots will ensure that it never goes without water, at least in our climate.
I had a Li in my yard which never fruited (maybe 1-2 would appear, then fall off). I transplanted it this past spring to a rental and it now has quite a few fruit on it (full sun in both locations). I’m not sure if that is due to all the sunny weather, but I suspect that the transplant had something to do with it. I remember reading that root pruning was one technique to push fruiting. Well, even though I was careful (used a hose for most of it), I’m sure I lost a lot of root during the transplant, so this was effectively a root-pruning…
Another thing I noticed on the large Sherwood is that it seems most productive on the horizontal branches (something many people have noted with other types of fruit trees). When jujube are shaded and/or crowded. they often try to grow up to get more sun. That could also contribute to the lack of fruit.
In the background of the above pic, there is an almost horizontal branch in the upper left corner of the pic. It is the most heavily laden one on the tree.
Edit: now that I think about it, the Sherwood that is producing for the first time (aside from a handful of poor fruit) was right next to the Li that was transplanted. I wonder if the accidental root pruning contributed to the heavy set in the Sherwood as well.
Edit #2: I added labels to the above pic. This row of jujubes is next to my driveway and gets almost complete sun, other than any shading from each other and themselves.