Is public data available for routes that enter/exit a certain airspace?
A free public resource would be the FAA's statistics page. I'm not sure if they have the specifics you need but they have a lot of data available. It would probably be easier to find data specific to the airports than it would for the whole artcc. Flight data doesn't usually include what airspace they pass through but where they depart and arrive.

There are commercial sites that have the raw data. FlightAware has full xml data for pretty much all scheduled flights going back several years. It's a treasure trove of data, it's a matter of extracting it. If you can write an api then  have options for using their data for a per-query fee. Their info page is here Their prices are in fractions of a penny, but I really know nothing about api's so I have no idea how quickly they would add up. It probably depends on how efficient the api is in getting the information with the least number of queries.