24-hour visa question

i am in qingdao, with a return flight back to the UK (via wuhan) on the 16th of august. my visa is an x-2 type with a single entry. i have to attend my brother's wedding in korea on the 13th of august and am hoping to return to china right on the 16th to fly back to the UK. unfortunately, given my visa is single-entry, i probably wont be allowed back in to catch my flight without another visa.

is the 24 hour free transit the best option for me?
can i apply for one in seoul or will it have to be done at the airport when i return from seoul? what is the cost?
i understand that with such a visa, i can legally fly from qingdao to wuhan as part of my departure. hope this is true.