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.
I went ahead and used large binder clips.
I pushed the two cabinets together, removed the clear windows adjacent to each other, wrapped the wood in that thick and pliable clear plastic shelf liner, then used binder clips every 3-4” across the inside of the whole frame of the windows, marrying the two cabinets together with a plastic seal. Worked like a charm and much less intensive.
Now, I did have to buy a jig saw and shave 1/4” off the inside edges of both top display windows/doors. They wouldn’t shut otherwise.