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Ok, soooo, update on this. I was right in my initial assessment that this stuff is, in fact, not powdery mildew at all, but is instead something else. After a little more in depth research, the appearance and behavior of this stuff seems to be the hallmark of Silver Leaf, most likely caused by silver-leaf whiteflies. So it's no wonder that the neem wasn't doing anything, cause this stuff isn't even a fungus at all. Supposedly, whatever toxin or poz load the flies carry with them turns the leaves a silvery color, beginning in the veins and spreading out to the rest of the leaf overtime if feeding keeps occurring.
The literature has said absolutely nothing regarding a cure, only prevention. It's not a deadly disease, but if severe enough it could and most likely would impact fruit production and quality. Fortunately, it isn't so bad for me, as you can see here in these images. It's only considered a serious disease for seedlings and younger plants, but if the plant is mature, or the closer it is to harvest, the less impact it has as the plant just continues to grow new foliage, allowing continued photosynthesis.
Just so long as the feeding stops, the plants should be fine and the spread should be slow or stopped entirely. Worst comes to worst, for the leaves that completely succumb to the silvering, I'll snip them off, but it's worth keeping the mildly infected ones since they're still functional, if at least partially.
The more you know.