Australian tourist refused tourist type? What now? HELP

Went to Seoul Chinese Visa Application center.

Applied for simple L tourist type with all documents provided (travel schedule, tickets, hotel bookings, passport photo, original Australia Passport and completed application form). This first application was not completed properly as it hadn't been signed at the end and the staff didn't catch it so the embassy rejected it and advised to redo.

Since urgent applied immediately again with complete application again and all documents provided once again with express same day service fee and this time was rejected for no apparent reason except for apply in home country Australia!

Before travelling to Korea I had contacted the Chinese embassy as well as the center in Australia and here in Korea. No one had stipulated such a stupid clause and even whilst there both times no one stated any such rule and I saw normal tourists applying too. The person I spoke to at the center didnt even understand how this is possible or why.....

Can I contact the embassy directly and make my case? Point out that I had contacted them and both centers+1st application they only said signature was missing etc?
Can I apply through a travel agency somewhere else? Maybe Busan in the South?

Should I try HK or Japan instead? Directly or travel agency is recommended?

This is HIGHLY infuriating! Everything is organised, attending exhibition, meeting friend and everything paid for and now LAST MINUTE they refuse for no real reason except this BS!!!! WTH!

WHAT can I do? PLEASE HELP!

(I've never been there. They would have ZERO reasons to reject eg money, criminal record, lack of documents etc.)