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Not sure if this is intentional, but when using the "inject" option to place the picker within a container, the picker's position is still being calculated relative to the document and not the container. It seems to me that if you are placing the picker within a container, you want to position it relative to the container (which should have position: relative). It's a quick fix if anybody agrees:
Within Picker.js, the function position() has a call to getCoordinates that should look like this:
element.getCoordinates(this.options.inject || document.body);