Symptoms

Checkbox List Choice control 'specify your own value' field not updating return value.
 

Diagnoses

The issue appears specific to using the control context part as a value. When using 'specify your own value' the state of its checkbox isn't updated until the control is interacted with elsewhere (toggling a different checkbox).
 

Resolution

What does appear to work is using the 'Choice Control -> Items -> Display' context part inside the For Loop, though this will return the items one at a time instead of in a delimited list. If you need them concatenated you can add the values up inside a Parameter (Param = Param]aChoice.Items.Display]) and then use that.