Welcome to FT. I understand your frustration, but if you consider this incident as "horrible customer service" then I recommend you stop flying airlines all together.

AA admitted a system issue and re-submitted your request, they say it can be 30 days but most of my partner airline missing mileage requests are completed within a week. Not sure what else you could accomplish by escalating further or emailing Doug Parker. Asking for EXP status immediately is unreasonable and I can see why AA said no.