You can actually use the bus system
I swear! If you need to get across the park, consult a bus map and hop on the bus that's most convenient for you. There are tons of them, and if you navigate properly, you're more than likely to be delivered straight to your destination. Plus, you get a free transfer if you hop onto a bus after using the subway. Just know not to rely on the bus being timely, especially later on in the day. They're not only subject to those vague scheduling delays that plague the subway, but also the insane traffic that plagues any motor vehicle in NYC.
[Photo via @mtanyctransit]