How would you get an answer/choice chosen within a quiz after submission to appear on separate slide within Storyline?

Your initial thoughts are right: use custom variables. It's really quite simple:

• For each question, create a custom variable.
  • I'd use a Text variable, which would allow you to indicate answers as A, B, C, or D; 1, 2, 3, or 4; or anything else you want.
• Add a trigger to each response that adjusts that question's variable so it indicates the answer. For example, clicking response "A" adjusts the variable to "A." 
• On the follow-up slide, use triggers with conditions to hilite the user's answer based on the value of the variable. 
  • You could hilite the chosen answer with a separate outlining object, or just create a custom "Chosen" state. 
  • For example, a trigger could change choice A to the Chosen state when the timeline starts with the condition that the associated variable = A. Separate triggers would do the same for the other choices. 

FYI: If you use the built-in Likert Survey questions, you'll need a Survey Results slide to have the responses sent to the LMS.

If you just want to use the results within the course, this post provides some guidance: TIP: Track Responses to Custom Questions or Surveys - Articulate Storyline Discussions - E-Learning Heroes