This is similar to what I had in mind, but rectangular instead of cylindrical, and that had a lip on the ends of the bar that slotted and locked into “C” plates on both ends.
But, unistrut bars across the backs of the cabinets also might do the trick, instead of bars in between.
I suppose I could put two unistruts across the backs of the enclosures, near the bottom and top of the window top half. That would stabilize it enough that you wouldn’t really be able to flex the fronts together.
Cabinets to each other, probably 3-4 stabilizers, 1 per corner of the windowed sections between the two cabinets.
“Aye, oh! Aye, oh!”