My experience is that if you explain to them that you are transiting from the US and show them your tickets/boarding passes from your other flights they will usually grant you the baggage allowance provided your stopover is less than 24 hrs. I did this once in Shanghai several years ago doing the airport switch and it was no problem. It is somewhat dependent on who you get at check-in but if you push hard enough they should give it to you... if not you can always resort to Danmairen's suggestion as a back up plan. :)
If you are staying in a hotel you do not need to go the police station as the hotel takes care of your registration. At check in they are required to take your passport and they fill out the required forms for you. If you are staying with a friend or in a private residence then you need to go to the police station to register