Wow those cabinets are cheaply built! I can only imagine how much coloration they add.
You seriously need to add a ton of bracing, but bracing has to be in tight to be effective. Either cut pieces about 1/32" oversize and tap into place with a hammer, or do something like - cut your brace about 1/4" oversize, then cut it in half with a miter cut. So you end up with 2 pieces like:
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/ /
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Then when you put them in place put glue and a clamp on the miter cut, the clamp will slide the two pieces down and outward ... putting tension on the walls.
Or even better, sell them and put the funds toward a kit from GR and build some decent cabs.