Fludubu used a cover panel as the headboard, but I’m quite sure you can apply the same to the LINNMON. However, unlike a cover panel the LINNMON is not full particleboard and does contain paper filling (honeycomb structure). Just knock on the table surface to locate sections where there is actual wood to secure your brackets. It’s usually along the sides and corners.
The LINNMON attachment is meant for joining two horizontal planes and would not have enough bite to hold a vertical plane.
Or you can use the BRIMNES headboard.
And add legs to it. Like this. You can cover up the open back with plywood or fabric if you find it unsightly.
As you mentioned that the bed would not be against a wall, if I were you, I would make additional shelves for the open back. And add a piece of wood at the bottom to create more storage. Use iron-on edge banding tape to cover up the exposed edges.
You’ll still need to secure it to the BRIMNES bed to prevent it from falling over. A few screws through the BRIMNES headboard’s legs to the bed and straight brackets on both sides should do the trick.