Used 144 hr visa, can I get 24 hr free transit too?

Hello,

I'm currently holding a 144 hr free entry, it expires on 4/1/17. Im in Shanghai until 3/28 then I'm leaving for Seoul on 3/28. From Seoul I fly to Taipei, however I will be leaving Taipei 4/11, 15 hrs layover in Shanghai and I will be exiting the airport, then flying 4/12 from Shanghai to San Francisco.

My question is because I've already used a 144 hr free entry, could I apply for a 24 hr free entry?