Any food container that was sturdy enough would work. I don't think an oatmeal container would be strong enough though. Nestle Quik probably would be if you glued more than one layer on it as the glue and fabric would make it stronger.
And if the container had a lid then you wouldn't need a lid stabilizer as the lid would keep the top wooden plaque in place (although any fabric at the top of the container may make the lid fit too snug.).
If you make something like this post pictures. I'd like to see it.