How can I keep the two sides of my king size adjustable bed together?

We have the same and mattresses moving has never been much of an issue. The little trouble we have seen, both of us stand by the bed and bump the mattresses toward each other. We do use sheets that cover both mattresses together so maybe that helps. Some sheets come as separate bottom sheets, but ours is one bottom attached to one top and we have it all tucked in together. Be sure your main frames are not moving. We bolted ours down so the frames would not move and that may also be a big help. We did it because the headboard we purchased had to be bolted down, so we discovered the bolting influence accidentally. Hope this helps Myrtis.

Take a wide piece of elastic and stretch it tight across the mattresses in at least three places, maybe near the top and the bottom and the middle and pin the ends of each elastic piece together. This should help to keep it in place.

Try bolting or tying the non moving center legs together.

Rubber shelf liner under the mattresses might help!

We had this same problem. Make sure both bases are straight and lined up squarely. Correcting this pretty much fixed our “canyon” problem

Could you insert a piece of wood, rubber, or similar item to the frame's interior edges, to force the twin box springs to fit tightly?

Naomie suggested rubber shelf liner; in that same vein, I thought of the non-slip liner you put under area rugs, mainly because that comes in wider sizes.

Adjust the iron plate connector, many split kings come with a connector. You can also use a non-slip mattress pad, they are grippy and can stop the sliding of the mattress. Also, you can use Non-slip tape under the mattress on the bed base. You can try these tricks to keep your best adjustable beds together.

you put them in the same fitted sheet to hold them together