If you paid for a transit visa that only permits 24 hour stays in China, you got a raw deal because the PRC offers visa free transit to pretty much everyone who isn't on their black list. Moreover, since neither rgn-pek nor pek-ewr entail any intermediate stops within the PRC, you'd be eligible for 72+ hours visa free transit in Beijing, assuming you hold a passport from one of the ~30 countries that qualify. While it sucks that CA only flies to RGN two days per week now, I think the reasonable course of action would be to make their current schedule work for you; Beijing is a pretty amazing place.