As long as the RP application was in the hands of the PSB on the 30th... you would still be ok. It needs to be submitted, not necessarily finished processing before the expiry date. 3 years ago, when I first transferred schools, the RP application was actually submitted on the final day (ie the day the old one expired), and approved a few days later. Given the "new 3 week" processing time for residency permits this year... that is a very good thing. Who in Beijing has said that to you? I know it is definitely not the case where I am in any way, and my understanding was that this was the same across the country. What is the problem now with you getting it processed? Is there any reason why it can't be submitted before the previous one expires? My understanding would be, that if that happens then you do not need any other visa to cover you while it is being processed. They will even be able to give you "official" paperwork confirming they have your passport and are processing the RP, potentially covering you for when you need to use the passport.