In your first paper, fig 1 (a), the "ready" box play the role of the "selected".
The universe tell you whether to select or not (it's not you missing events). It just tells it to you without giving any info on the underlying state. You can build a ready box without problem, and experimenters did, and that's all that is needed to break CHSH.
You've got to see it in an abstract way. Nature's is fuzzy and experimenters will always have to define box boundaries (spatial, temporal, and entanglement-pair selection boxes). This defining create conditioning which makes breaking bell inequalities something totally normal, expected and meaningless.
A related concept that may help you see it is https://en.wikipedia.org/wiki/Correlated_equilibrium :
In a game of Chicken, you can get a better correlations between your actions that would seemingly be possible, by using a random variable oracle to coordinate. No information exchange needed. Measurement devices are kind of playing a continuous version of this game.