I can't seem to get the trigger 'When the state [BUTTON A] is Visited' to work.

As Andrew stated, if you want to change the state of the continue button based on an activity that happens on the other slide (like visited state change) you need to use a T/F variable. 

You don't necessarily need to have a T/F variable for each visited object. You could have a single variable that changes when the states of all those objects are visited. Then when you go to the other slide, you can change the state of the continue button when the timeline of the slide starts on the condition of the T/F variable.