Bed hanger upgrade

We bought a very nice steel bunk bed for my son,
But, although the frame is nice and strong, the bars, that the mattress rests on
are wholly insistent, even for a child, never mind a teenager.

If you look at the photo, the metal tube has a plastic end, with two little teeth,
Which snap into the frame, but only loosely grip the metal tubes (FAIL).

So I designed these 'hooks' to hold inexpensive, and readily available Stud partitioning timber.
The main advantage is, that the wood is smo