Are you being specific to human action or taking empiricism vs. apriorism in a more general sense?
Professor Casey has asked for a quick email to let him know if someone has posted a question. I don’t remember where it is posted I will see if i can find it for you.
Personally, I believe the distinction between a priori knowledge and empirical knowledge is somewhat questionable given that the idea that one can even have empirical knowledge starts from and as you intimated the problem of variables, often ends in a priori reasoning. I think it is fair to say they both have merit but to prove one is superior to the other (general sense) is beyond the scope of my intellect.
Analytic a priori statements are based on definitions and not necessarily reality. Take the statement: Shmoos are delicious, and eager to be eaten. To say that is not based on reality is saying the definition is false. The argument it self seems to be a non sequitur.
If you are looking for specific answers, it might help professor Casey if you give him some examples so he can know exactly what you’re looking for. Sorry I couldn’t be of any help but I look forward to his answer.