Your school international office is wrong. Using AP does not affect your H1 working status even if the parolee I-94 expired. You can continue to work legally until the H1 I-94/approval notice expires and just extend your H1 before the H1 expires and you will be H1 status again after the H1 is approved. Here is INS (USCIS) official document concerning this issue. You just print it out and show the document to your international office, emphazing the Question 3 and Q4 in this document.
http://shusterman.com/h1blvisasmemoworkingadvanceparole.html