Help prevent cabinet tip over!

We had some leftover IKEA Besta wall shelf units and I told my wife they would probably make a great sofa table if we put 3 of them next to each other behind the sofa. So I got some hinges and found matching door fronts. Everything was great until I opened one and it promptly fell forward on me.

No problem, if I screw them together the weight will prevent the tip over! Nope, now all three tip. All good, if I weigh them all down that'll work. So I added a 2x8 along the length of the cabinets and PL Premium'd the cabinets on. In my genius, I left a 2 inch "toe kick" and butted the lumber to the back of the cabinets. Great, now it's WORSE.

Right now I have a bunch of shims shoved in to tip the unit back a little and added a bunch of heavy objects inside the cabinets to weigh them down. It works for now, but I'd like something more permanent that would allow us to reposition the cabinet without having to re-shim all the time.

What is a better way to secure this down? I don't trust my genius ideas anymore.

https://preview.redd.it/bju4zkzy5qxf1.jpg?width=4284&format=pjpg&auto=webp&s=9f885fcdad458b58d84db60427d71880fad9e146

https://preview.redd.it/ep6crmzy5qxf1.jpg?width=4284&format=pjpg&auto=webp&s=3f185b15c899e9d309c452d572b2b64f6853d91c