Looks like TS is in deeeeeeeep shit.
Your posting has already been decided, so you will still go to the next unit. They cannot keep you in BMT just because some documents are missing.
Your PS should have known better when he hands out anything to thousands of recruits. You will not be the only person losing the documents.
Just get some $%#%^&$, and a new set will be printed from the centralised data base. All you have done is created some inconvenience, but that's what NS clerks are for. They don't chiongsua so have to do all this rubbish like generating more documents for NSFs who sacrifice more.