@technickly We are looking to do the same thing - publish the experience id and activity id values to a dedicated AA var. The guidance we were given was we would want to publish that in a listvar (which you get dedicated ones out of the box) and in essence you want to publish the activity id and experience id that is received via response tokens to the assigned listvar. Keep in mind, there might be multiple campaigns firing on the same URL, so this listvar will allow you to capture all campaign data (up to 255 characters, I believe) using some delimiter to separate campaigns, e.g. [123456:0|345678:1, etc.]
@technickly as @yza085 shared, you should use response tokens, in this case the activity name/id and the experience name/id for what is displayed. You will need to set up a rule in Launch that listen for the Adobe Target success event to grab the response tokens and place somewhere you can pick it up to send to Adobe Analytics as an evar. If you are going to have multiple experiences on the page you can use a list var which will be automatically slice it in Adobe Analytics, or you can set it into an evar and create a classification rule to slice it based on pipe delimitator as an example.