Potential expatriation to Ulsan, South Korea

Hello,

After living in Singapore for a little over year, our expatriation is coming to an end and my husband is considering an opportunity in Ulsan, Korea. 
We have 2 girls, a 5 year-old and an 8 year-old. 
Housing is no issue, he is being offered a furnished apartment within walking distance of the shipyard. 
Schooling seems to be a problem : the hyunday foreign school has a waiting list for my 5 year-old.
8 year-old is no issue.
I contacted the French school La fontaine, because we are a French/American family but the job wouldn't be for Total or Technip so it's not possible.

I have reservations about going to Ulsan if I can't get my kids in school there.
Does anyone have suggestions ? Are there other schools ?

Thanks so much in advance,
Anne-Claire